大学高数英文版练习题-学生
（完整版）英文数学题（1）
（完整版）英文数学题（1）1、In 2004, 16 June falls on a Wednesday. On what day of the week will 16 June fall in 2010?2、In a magic square the sum of the numbers in each row, in each diagonal and in each column are equal. In this magic square the value of x is:3、If half of a number is 30, then three-quarters of that number is____.4、The sum of the digits of the following product999×5555、Three positive integers have a sum of 28. The greatest possible product that these integers can have is_____.6、Jack was trying to tessellate regular pentagons. He managed the following figure.The size of angle .a. is______.7、If the area of the shaded region of the regular hexagon in the diagram below is 36 cm2, the area of the whole hexagon in cm2 is_____.8、In what follows, □and Δare different numbers.When 503 is divided by □the remainder is 20.When 503 is divided by Δ the remainder is 20.When 493 is divided by □x Δthe remainder is_____.9、A lady, her brother, her son and her daughter (all related by birth) played volleyball. The worst player's twin (who is one of the four players) and thebest player are of opposite sex.The worst player and the best player are of the same age.Who cannot be the worst player(s)?A) brother only B) daughter onlyC) son and daughter only D) lady and daughter onlyE) lady only10、If you continue the given number pattern, in what row and in what position in that row will the number 320 be?1 -------------- row 12 3 -------------- row 24 5 6 -------------- row 37 8 9 10 -------------- row 4The answers are given in the order of row ; position.参考答案：1、Wednesday2、123、454、27（求数位上上的数字之和）5、28=9+9+10，因此答案为8106、36度7、1088、503-20=483 483=3×7×23＝21×23，因此□x Δ＝483，因此此题余数是10.9、D 10、25，201、Did you know? In the decimal number system (base 10) ten different digits, 0 to 9, are used to write all the numbers. In the binary number system (base 2) two different digits are used, i.e. 0 and 1.Which one of the following numbers is not a valid number in theoctal number system (base 8)?A) 128 B) 127 C) 126 D) 125 E) 1243、The number of diagonals that can be drawn in a regular polygon with twenty sides (icosagon) is_____.4、If a and b are integers, 10Ä3=1,152Ä7=3, and then 379Ä6 is equal to_____.5、Two numbers are in the ratio 2 : 3. When 4 is added to each number the ratio changes to 5 : 7.The sum of the two original numbers is____.6、The greatest number of Mondays which can occur in 45 consecutive days is____7、Saul plays a video game in which he scores 4 for a hit and lost 6 for a miss. After 20 rounds his score is 30. The number of times he has missed is____.8、Three girls A, B and C run in a 100 m race. When A finishes,B is 10 m behind A and when B finishesC is 20 m behind B. How far in metres was C from A when A finished?(Let’s assume all the athletes run at a constant speed)9、The areas of the faces of a rectangulabox are 84 cm2 , 70 cm2and 30 cm2.The volume of the box in cm3 is____.10、You have 3 weights: 1 kg, 3 kg and 9 kg as well as an equal arm balance, as shown. How many different weight objects can you weigh with these three?[Remember the weights may be placed on either side]参考答案：1、A 考察我们学过的简单的进制问题，显然8进制中没有8出现2、B 用排除法3、170 找规律，公式为n×（n-3）÷24、1 定义新运算，就是求379÷6的余数。
英语数学题(中英文)
英语数学题班级： 姓名：1、今天是星期四，101000天后是星期几？Today is Thursday, what day is 101000 days later?2、某班男女人数相等，喜欢足球的学生中51是女生，喜欢足球的男生占全班人数的41。
已知不喜欢足球的女生有21人，喜欢足球的男生有（ ）人。
The number of boys and girls in a class is equal, one fifth of the students who like football are girls, and the boys like football are one quarter of the whole class. There are 21 girls who are not fond of football, then ( ) boys like football.3、某列火车通过长为82米的铁桥用了22秒，如果火车速度加快一倍，它通过706米的铁桥就用50秒，火车的长度是（ ）。
The train go through a bridge with 22 seconds which length is 82 meters , if the train ’s speed double, it go through 706 meters ’ bridge with 50 seconds, the length of the train is ( ).4、在黑板上写了若干个从1开始的连续自然数1,2,3,4,……,后来擦掉其中一个，剩下数的平均数是13139,擦掉的自然数是（ ）。
Written on the blackboard several consecutive natural numbers from the beginning of 1 1,2,3,4,...... , then wipe one of them, the average number of the remaining number is 13139, the wiped natural number is ( ). 5、A 、B 、C 、D 、E 五人在一次满分为100分的考试中，A 得94分，B 是第一名，C 的得分是A 与D 的平均分,D 得了五人的平均分，E 比C 多2分，是第二名，则B 得了（ ）分。
英文版-微积分试卷答案-(1)
（考点：经济函数，课本4.8节。
此题型为常考题，属于送分题，大家可以做相应的4.8节的练习加以巩固）9、State the second derivative test theorem testing maximum and prove it.Suppose is continuous near c''f If and , then has a local maximum at c .'c f （)=0''c f （)< 0Proof: Because near c and so is concave downward near ''c f （)< 0f c . This means that the graph of lies below its horizontal tangent at c and so has a local maximum at c .10、Show that the equation has at most one root in the 3150x x c -+=interval.[2,2]- Suppose the equation has two root in 3150x x c -+=1212,and x x x x <the interval .12,[2,2]x x ∈-Let then there exist 3F()15x x x c =-+12F()F()=0x x =Using the Rolle’s Theorem we can know that there exist one number c can satisfy12F'(c)0(,)c x x =∈2F'()3150[2,2]x x when x =-<∈-But , Therefore, the suppose is wrong. 2F'()3150[2,2]x x when x =-<∈-Then the equation has at most one root in the interval3150x x c -+=.[2,2]（考点：罗尔地理。
Unit 2小测(高数V2
Unit 2小测（高数V2您的姓名： [填空题] *_________________________________Choose the best item to complete each of the following sentences.1. All the students in Mrs.Black’s class are working very hard in order to___themselves in English. [单选题] *expectimprove(正确答案)comparelearn2. Mary enjoys a(n)_____ability to sing well. [单选题] *A.styleB.unfortunateD.natural(正确答案)C.glad3. Ann is wearing a beautiful dress,and Mary a _____one. [单选题] *A.similar(正确答案)B.realC.fluentD.rude4. They teach you the ____ you need to become a successful journalist. [单选题] *A.conversationC.detailB.skills(正确答案)D.headline5. When he wants to smoke, he forgets the fact that smoking _____ his health. [单选题] *catesB.cheatsD.respectsC.affects(正确答案)6. The teacher____ Tom’s homework with Mike’s and found little difference. [单选题] *pared(正确答案)B.experiencedC.sensedD.decided7. I don’t have the time and _____ to disagree with her,as I have a lot of work to do. [单选题] *A.responsibilityB.decisionC.accountD.energy(正确答案)8. This book gives all kinds of useful____ on how to repair bikes. [单选题] *A.sensermation(正确答案)B.savingD comfortTranslate the following into English9. 假如你让他待在你家，你就是在自找麻烦。
大学高数英文版练习题-学生
（D） 1 , 0 , and 1
(13) If y ax 2 b is strictly increasing in (0 , ) ，then a , b should be satisfied（ ）. （A） a 0 , b 0 （B） a 0 , b R （C） a 0 , b 0 （D） a 0 , b R (14) 2 is the（ ）for y x 3 3 x 2 6 x 2 on [1, 1] . （A）local maximum （B）local minimum ）.
x , then in the open interval (1 , 1) （ ）. 1 x2 （A）y is increasing （B）y has a relative maximum
（C）y is decreasing （D）y has a relative minmum (5) If f ( x ) xe x , then at x 1 （ ）. （A）f is increasing （B）f has a relative maximum （C）f is decreasing （D）f has a relative minmum (6) Let f ( x) continuous ，and f (0) = 0， lim f ( x) =1，then f (0) is （ ）value of f ( x) .
ba f ( ) f (b) f (a ) f (b) f (a ) (C) f ( ) ba (3) If x 0 , then （ ）.
(A)
(B) f ( ) f (b) f (a ) (D) f ( ) f (a ) f (b)
数学英语练习题
数学英语练习题### 数学英语练习题#### 数学部分一、选择题1. What is the value of \( 2^3 \) ?- A. 4- B. 6- C. 8- D. 102. If the perimeter of a square is 20 units, what is the length of one side?- A. 5 units- B. 4 units- C. 3 units- D. 2 units3. Solve for \( x \) in the equation \( 3x - 7 = 8 \) . - A. 3- B. 5- C. 7- D. 9二、填空题1. The sum of the first \( n \) natural numbers is given by the formula \( \frac{n(n+1)}{2} \). If \( n = 10 \), the sum is ______.2. The area of a rectangle is calculated by multiplying its length by its width. If the area is 48 square meters and the width is 8 meters, the length is ______ meters.3. If a right triangle has legs of 3 and 4 units, the hypotenuse is \( \sqrt{3^2 + 4^2} \), which equals ______ units.三、解答题1. A store has a sale where all items are 20% off. If a jacket originally costs $100, what is the sale price?2. A train travels at a constant speed of 60 miles per hour. How long will it take to travel 180 miles?3. A company has 120 employees. If the company decides to increase the workforce by 25%, how many new employees will be hired?#### 英语部分一、选择题1. Which word is a synonym for "diligent"?- A. Careless- B. Lazy- C. Hardworking- D. Idle2. The phrase "break the ice" is used to describe what?- A. Shattering a frozen lake- B. Starting a conversation- C. Cooling a room- D. Freezing a beverage3. The word "altruistic" is most closely related to which of the following?- A. Selfish- B. Generous- C. Greedy- D. Stingy二、填空题1. The word "____" can be used to describe someone who is always ready to help others.- (Hint: Begins with 'w')2. The past tense of "begin" is ______.3. The phrase "____" is used to express that something is very easy.- (Hint: Contains the word 'piece')三、作文题Write a short essay about the importance of learning a secondlanguage. Your essay should include:- The benefits of being bilingual.- How learning a new language can broaden one's perspective. - Your personal experience or opinion on language learning.Please attempt the above questions to test your understanding of mathematical concepts and English language skills. Remember, practice makes perfect!。
大学生英语练习题
大学生英语练习题### 大学生英语练习题#### 阅读理解Passage 1: The Benefits of BilingualismBilingualism, the ability to speak two languages fluently,has been linked to numerous cognitive benefits. Research suggests that bilingual individuals have enhanced problem-solving skills, better multitasking abilities, and improved memory. Moreover, learning a second language can delay the onset of dementia and Alzheimer's disease. Despite these advantages, many people struggle with the process of learning a new language due to various challenges such as time constraints and lack of exposure.Questions:1. What cognitive benefits are associated with bilingualism?2. How does learning a second language impact the aging brain?3. What are some challenges faced by individuals learning a new language?#### 词汇练习Word List:- Cognitive (adj.) 认知的- Enhanced (adj.) 加强的，提高的- Multilingual (adj.) 多语言的- Dementia (n.) 痴呆- Onset (n.) 开始，发作Fill in the Blanks:1. The use of technology has greatly _______ our daily lives.2. Being a _______ speaker can open up many job opportunities.3. Early signs of _______ can be subtle and easily overlooked.4. The _______ of a new project can be stressful for the team.#### 语法练习Subject-Verb Agreement:Choose the correct form of the verb to complete the sentences.1. Either the students or the teacher _____ (is/are) responsible for the project.2. Neither the books nor the articles _____ (has/have) been read by the students.3. A number of books _____ (is/are) on the table, but a number of students _____ (is/are) in the library.#### 写作练习Topic: The Impact of Technology on EducationWrite an essay discussing the positive and negative impactsof technology on education. Your essay should include an introduction, body paragraphs with supporting details, and a conclusion. Use a variety of vocabulary and complex sentencestructures to express your ideas clearly.Sample Introduction:In recent years, technology has revolutionized theeducational landscape, offering both unprecedented opportunities and challenges. This essay will explore the various ways in which technology has transformed learning experiences and the implications of these changes.Sample Body Paragraph:One of the most significant advantages of integrating technology into education is the accessibility of information. With the internet, students can access a wealth of knowledgeat their fingertips, which can enhance their understanding of various subjects. However, this ease of access also poses a challenge in terms of information overload and the need for critical evaluation of sources.Sample Conclusion:In conclusion, technology has undeniably reshaped the educational sector, offering both benefits and drawbacks. While it is crucial to harness the positive aspects of technology to enrich the learning process, it is equally important to address the potential pitfalls to ensure a balanced and effective educational experience.#### 完型填空Read the following passage and fill in the blanks with the most appropriate word from the options provided.In today's fast-paced world, time management is crucial for success. It is not just about completing tasks on time, but also about __1__ (A. prioritizing B. procrastinating) them effectively. Effective time management can lead to increased productivity and less stress. However, many people struggle with __2__ (A. managing B. avoiding) their time well, often due to distractions or poor planning.Answers:1. A. prioritizing2. A. managing#### 翻译练习Translate the following sentences from English to Chinese and vice versa.English to Chinese:1. The rapid development of technology has brought about significant changes in our daily lives.2. Environmental protection is a global issue that requires the collective effort of all nations.Chinese to English:1. 教育对于一个国家的发展至关重要。
做一些数学练习题英文
Math Practice ExercisesI. Arithmetic1. Calculate: 345 + 6782. Subtract: 1000 4323. Multiply: 56 × 784. Divide: 144 ÷ 125. Find the square root of 646. Calculate: (8 + 3) × 6 57. Simplify: 18 ÷ (2 + 1)8. Evaluate: 7^39. Find the sum of the first 10 even numbers.10. Calculate the product of the first 5 odd numbers. II. Algebra1. Solve for x: 3x + 7 = 252. Simplify the expression: 4(x 3) + 2x3. Expand and simplify: (2x + 5)(x 3)4. Solve the equation: 5x 3 = 2x + 125. Find the value of x: 2(x 4) + 3x = 216. Solve the system of equations:2x + 3y = 8x y = 37. Factorize: x^2 5x + 68. Solve the inequality: 3x 7 > 2x + 49. Simplify the expression: (3x^2)^2 ÷ (9x)10. Solve for x: |x 4| = 5III. Geometry1. Find the area of a rectangle with length 8 units and width 5 units.2. Calculate the perimeter of a square with side length 7 units.3. Find the volume of a cube with side length 6 units.4. Determine the circumference of a circle with radius 10 units.5. Calculate the surface area of a sphere with radius 5 units.6. Find the slope of the line passing through points (2, 3) and (5, 7).7. Write the equation of a line with slope 2 and yintercept 5.8. Find the midpoint of the line segment with endpoints (4, 3) and (2, 5).9. Determine the angle between the lines y = 2x + 1 and y = 0.5x + 3.10. Calculate the distance between the points (3, 8) and (5, 2).IV. Trigonometry1. Find the sine of 45°.2. Calculate the cosine of 30°.3. Determine the tangent of 60°.4. Solve for x: sin(x) = 0.55. Find the value of x: cos(x) = 0.66. Calculate the value of sin(2θ) if sin(θ) = 0.3.7. Determine the length of the hypotenuse in a right triangle with legs of lengths 6 units and 8 units.8. Find the angle θ in a right triangle if the op posite side is 5 units and the hypotenuse is 10 units.9. Solve for x: 2sin(x) 1 = 010. Calculate the value of cos^2(x) + sin^2(x).V. Probability and Statistics1. A coin is tossed 3 times. What is the probability of getting exactly 2 heads?2. A standard sixsided die is rolled. What is the probability of rolling a 4 or a 6?3. In a class of 30 students, 18 are girls. What is the probability that a randomly selected student is a boy?4. Calculate the mean of the following numbers: 4, 7, 10, 12, 15.5. Find the median of the data set: 3, 8, 5, 12, 7, 9.6. Determine the mode of the following numbers: 2, 5, 7, 5, 8, 9, 5, 11.7. Calculate the variance of the data set: 6, 8, 10, 12, 14.8. Find the standard deviation of the following numbers: 9, 12, 15, 18, 21.9. A survey of 200 people found that 120 preferred coffee to tea. What is the probability that a randomly selected person prefers coffee?10. In a binomial experiment with n = 10 and p = 0.4,find the probability of getting exactly 6 successes.VI. Precalculus1. Evaluate the expression: (3^2)^3 ÷ 3^43. Write the expression as a single logarithm: log(5x) + log(3) log(2x)4. Solve the equation: 4^x = 165. Expand the binomial expression: (a + b)^46. Find the domain of the function f(x) = 1 / (x^2 9)7. Determine the range of the function g(x) = 2x^2 + 4x + 58. Solve the system of inequalities:2x + 3y ≤ 6x y > 29. Graph the function h(x) = |x 2| 310. Find the inverse function of f(x) = (x + 3) / 2.VII. Calculus1. Find the derivative of f(x) = x^3 2x^2 + 4x 72. Calculate the second derivative of g(x) = sin(x)3. Evaluate the definite integral: ∫(from 0 to π) sin(x) dx4. Find the limit as x approaches 0 of (sin(x) / x)5. Determine the critical points of the function h(x) =x^4 8x^3 + 18x^26. Find the area under the curve y = e^x from x = 0 to x= 27. Calculate the volume of the solid obtained rotatingthe region bounded y = x^2, y = 4, and x = 0 about the xaxis.8. Solve the differential equation: dy/dx = 3x^2 2x9. Find the antiderivative of f(x) = 1 / (x^2 + 1)10. Determine the arc length of the curve y = ln(x) fromx = 1 to x = e.VIII. Logic and Reasoning1. If all cats are mammals and some mammals are not cats, which of the following must be true?All mammals are cats.No mammals are cats.Some mammals are cats.None of the above.2. Given the statement "If it rains, then the ground is wet," which of the following is a contrapositive?If the ground is wet, then it rains.If it does not rain, then the ground is not wet.If the ground is not wet, then it does not rain.None of the above.3. Determine whether the following argument is valid:All birds have wings.Penguins are birds.Therefore, penguins have wings.4. If p and q are statements, which of the following represents the negation of "p and q"?p or qnot p and not qnot p or not qp and not q5. Which of the following is an example of a conditional statement?All squares are rectangles.I will go to the store if I need milk.The sun is shining.None of the above.6. If A is a subset of B and B is a subset of C, which of the following must be true?A is a subset of C.C is a subset of A.A is equal to C.None of the above.7. Given the statement "All students who study hard pass their exams," which of the following is a converse?All students who pass their exams study hard.No students who study hard fail their exams.Some students who pass their exams do not study hard.None of the above.8. Which of the following is an example of a tautology?p or not pp and not pp or qp and q9. If the statement "All triangles have three sides" is true, which of the following must also be true?All shapes with three sides are triangles.No shapes with more than three sides are triangles.Some shapes with three sides are not triangles.None of the above.10. Determine whether the following biconditional statement is true or false: "A number is even if and only if it is divisible 2."答案I. Arithmetic1. 10232. 5683. 43684. 125. 86. 397. 68. 3439. 9010. 945II. Algebra1. x = 62. 10x 63. 2x^2 11x 154. x = 35. x = 36. x = 2, y = 17. (x 2)(x 3)8. x > 49. 4x^310. x = 1, x = 6 III. Geometry1. 40 square units2. 28 units3. 216 cubic units4. 62.83 units5. 314.16 square units6. 17. y = 2x + 58. (1, 2)9. 90°10. 8.06 unitsIV. Trigonometry1. 0.7072. 0.63. 1.7324. 30°, 150°5. 53.13°6. 0.67. 10 units8. 30°9. x = 30°, 150°10. 1V. Probability and Statistics1. 3/82. 1/33. 6/10 or 0.64. 95. 7.56. 57. 48. 2.2369. 3/5 or 0.610. 0.2304VI. Precalculus1. 272. 5/63. log(15x)4. x = 25. a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^46. x ≠ 3 and x ≠ 37. All real numbers8. No solution9. arctan(x) + C10. 1VII. Calculus1. f'(x) = 3x^2 4x + 42. g''(x) = sin(x)3. 24. 15. x = 1, x = 3.56. 6.3897. 50.2658. y = x^3 x^2 + C9. arctan(x) + C10. 1.299VIII. Logic and Reasoning1. Some mammals are cats.2. If the ground is not wet, then it does not rain.3. Valid4. Not p or not q5. I will go to the store if I need milk.6. A is a subset of C.7. All students who pass their exams study hard.8. p or not p9. No shapes with more than three sides are triangles.10. True。
2023大学_数学专业英语试题及参考答案
2023数学专业英语试题及参考答案数学专业英语试题一、词汇及短语1. For a long period of the history of mathematics, the centric place of mathematical methods was occupied by the logical deductions “在数学史的很长的时期内，是逻辑推理一直占据数学方法的中心地位”2. An equation is a statement of the equality between two equal numbers or number symbols.equation ：“方程”“等式”等式是关于两个数或数的符号相等的'一种陈述3. In such an equation either the two members are alike, or become alike on performance of the indicated operation. 这种等式的两端要么一样，要么经过执行指定的运算后变成一样。
注“two members”表等号的两端alike 相同的一样的On the performance of …中的“on”引导一个介词短语做状语Either…or…4. is true “成立”5. to more and change the terms移次和变形without making the equation untrue 保持方程同解数学专业英语试题二、句型及典型翻译1. change the terms about 变形2. full of ：有许多的充满的例 The streets are full of people as on a holiday(像假日一样，街上行人川流不息)3. in groups of ten…4. match something against sb. “匹配”例 Long ago ,when people had to count many things ,they matched them against their fingers. 古时候，当人们必须数东西时，在那些东西和自己的手指之间配对。
数学练习题英文
数学练习题英文Math Exercise Questions1. John has 5 apples and he gives 2 apples to his friend. How many apples does John have now?2. A rectangle has a length of 7 cm and a width of 3 cm. Calculate the area and perimeter of the rectangle.3. If 4 pencils cost $6, how much would 8 pencils cost?4. Sharon is twice as old as her sister Jennifer. If Jennifer is now 12 years old, how old is Sharon?5. Solve the following equation for x: 3x + 5 = 17.6. In a class of 30 students, 15 are boys. What is the ratio of boys to girls in the class?7. Tom bought a shirt that costs $25, but he received a 20% discount. How much did Tom pay for the shirt?8. A box contains 10 red balls, 5 blue balls, and 8 green balls. What is the probability of randomly selecting a blue ball from the box?9. A train travels at a speed of 60 km/h for 2 hours and then increases its speed to 80 km/h for the next 3 hours. What is the total distance traveled by the train?10. The perimeter of a square is 40 cm. Calculate the length of each side of the square.11. A bookstore has 120 books. If 20% of the books are fiction, how many fiction books are there in the bookstore?12. The sum of three consecutive numbers is 72. What are the three numbers?13. If a toy car is scaled down to 1/18 of its actual size, and the actual car measures 36 cm in length, what is the length of the scaled-down toy car?14. A garden is in the shape of a triangle with a base of 12 meters and a height of 8 meters. Find the area of the garden.15. The price of a laptop is $800. If the price increases by 10%, what is the new price of the laptop?16. Solve the following equation for x: 2x - 3 = 9.17. A rectangular prism has a volume of 240 cubic meters. If the length is 10 meters and the width is 6 meters, what is the height of the prism?18. If Sally saves $20 per week, how much money will she have saved after 12 weeks?19. The ratio of boys to girls in a class is 3:5. If there are 48 students in the class, how many boys are there?20. A recipe requires 2 and a half cups of flour. If 2 cups of flour weigh 500 grams, how much does 2 and a half cups of flour weigh?These math exercise questions are designed to test your problem-solving skills and mathematical knowledge. Remember to show your calculations and provide clear explanations for your answers. Practice these questions toenhance your mathematical abilities and improve your accuracy in solving various mathematical problems.。
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（C）global maximum （D）global minimum (15) Which of the following curves hasthe inflection point (0, 0) ? （ （A） y x
2
（B） y x
3
（C） y x
4
（D） y x
2 3
2. Find the Local maximum and minimum for y 2 x 3 6 x 2 18 x 7 . (10 pts.)
（C）is decreasing in (o, + )
(D) is increasing in（0, + ）
(10) If in (a, b) f ( x) 0 , f ( x) 0 , then y f ( x) is（ ）in (a, b) . （A）decreasing and convex up （B）decreasing and convex down （C）increasing and convex up （D）increasing and convex down (11) What are all values of x for which the function f defines by
（D） 1 , 0 , and 1
(13) If y ax 2 b is strictly increasing in (0 , ) ，then a , b should be satisfied（ ）. （A） a 0 , b 0 （B） a 0 , b R （C） a 0 , b 0 （D） a 0 , b R (14) 2 is the（ ）for y x 3 3 x 2 6 x 2 on [1, 1] . （A）local maximum （B）local minimum ）.
3. Find the intervals of concavity and convexity and the inflection points for y xe x . (10 pts.)
4. Prove the following inequalities: (2*10=20 pts.)
x 0
(A) local maxima (C) not local extreme (7)
(B) local minima (D) maybe local extreme
y x 3 12 x 1 （ ）in its domain.
（A） is increasing （B） is decreasing （C）is concave （D）is convex (8) If y f ( x) obtain local maximum at x x0 ，then it must be（ ）. （A） f ( x0 ) 0 （B） f ( x0 ) 0 （C） f ( x0 ) 0 且 f ( x0 ) 0 （D） f ( x0 ) = 0或 f ( x0 ) 不存在 (9) f ( x) x ln x （ ） 1 1 （A）is decreasing in (0, ) （B）is decreasing in ( ) e, e
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1
Test 4
Date___________ Class___________
Name___________ Score__________
ba f ( ) f (b) f (a ) f (b) f (a ) (C) f ( ) ba (3) If x 0 , then （ ）.
(A)
(B) f ( ) f (b) f (a ) (D) f ( ) f (a ) f (b)
(A) e x e x (B) e x x 1 (C) e x e( x 1) (D) ln(1 x) x (4) If y
Test 4
Date___________ Class___________
Name___________ Score__________
1. Choose the best answer for each question. (4*15 = 60pts.) (1) If f :[a, b] R, satisfies: (1) f is continuous on [a, b]; (2) f is differentiable on (a, b); (3) f (a) = f (b), then there exists at least one point (a, b) such that f ( ) （ ）. (A) 0 (B) 1 (C) f ( ) f (a ) (D) 1
x , then in the open interval (1 , 1) （ ）. 1 x2 （A）y is increasing （B）y has a relative maximum
（C）y is decreasing （D）y has a relative minmum (5) If f ( x ) xe x , then at x 1 （ ）. （A）f is increasing （B）f has a relative maximum （C）f is decreasing （D）f has a relative minmum (6) Let f ( x) continuous ，and f (0) = 0， lim f ( x) =1，then f (0) is （ ）value of f ( x) .
f ( x) x 3 3 x 2 9 x 7 is increasing? ( ).
（A） 3 x 1 （B） 1 x 1 （C） x 3 or x 1 （D） x 1 or x 3 (12) If f is the function defined by f ( x) 3 x 5 5 x 4 , what are all the x–coordinates of points of inflection for the graph of f ? ( （A） 1 （B） 0 and 1 （C） 1 ).
(1) tan x > x if x 0, . 2
(2) 1
1 x 1 x ( x 0) . 2
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(2) If f :[a, b] R, satisfies: (1) f is continuous on [a, b]; (2) f is differentiable on (a, b); then there exists at least one point (a, b) such that f ( ) （ ）.