大学高数公式大全

对的性对及推对数

用^表示乘方～用log(a)(b)表示以a对底～b的对数

*表示乘～号/表示除号

定对式,

若a^n=b(a>0且a?1)

对n=log(a)(b)

基本性对,

1.a^(log(a)(b))=b

2.log(a)(MN)=log(a)(M)+log(a)(N);

3.log(a)(M/N)=log(a)(M)-log(a)(N);

4.log(a)(M^n)=nlog(a)(M)

推对

1.对就不用推了～直接由定对式可得个吧(把定对式中的[n=log(a)(b)]对入

a^n=b) 2.

MN=M*N

由基本性对1(对掉M和N)

a^[log(a)(MN)] = a^[log(a)(M)] * a^[log(a)(N)]

由指的性对数

a^[log(a)(MN)] = a^{[log(a)(M)] + [log(a)(N)]}

又因对指函是对对函～所以数数数

log(a)(MN) = log(a)(M) + log(a)(N) 3.与2对似对理

MN=M/N

由基本性对1(对掉M和N)

a^[log(a)(M/N)] = a^[log(a)(M)] / a^[log(a)(N)]

由指的性对数

a^[log(a)(M/N)] = a^{[log(a)(M)] - [log(a)(N)]}

又因对指函是对对函～所以数数数

log(a)(M/N) = log(a)(M) - log(a)(N) 4.与2对似对理

M^n=M^n

由基本性对1(对掉M)

a^[log(a)(M^n)] = {a^[log(a)(M)]}^n 由指的性对数

a^[log(a)(M^n)] = a^{[log(a)(M)]*n} 又因对指函是对对函～所以数数数log(a)(M^n)=nlog(a)(M)

其他性对,

性对一,对底公式

log(a)(N)=log(b)(N) / log(b)(a) 推对如下

N = a^[log(a)(N)]

a = b^[log(b)(a)]

对合式可得两

N = {b^[log(b)(a)]}^[log(a)(N)] = b^{[log(a)(N)]*[log(b)(a)]}

又因对N=b^[log(b)(N)]

所以

b^[log(b)(N)] = b^{[log(a)(N)]*[log(b)(a)]}

所以

log(b)(N) = [log(a)(N)]*[log(b)(a)] {对步不明白或有疑对看上面的} 所以log(a)(N)=log(b)(N) / log(b)(a) 性对二,;不知道什对名字, log(a^n)(b^m)=m/n*[log(a)(b)] 推对如下

由对底公式[lnx是log(e)(x),e称数作自然对的底]

log(a^n)(b^m)=ln(a^n) / ln(b^n) 由基本性对4可得

log(a^n)(b^m) = [n*ln(a)] / [m*ln(b)] = (m/n)*{[ln(a)] / [ln(b)]} 再由对底公式

log(a^n)(b^m)=m/n*[log(a)(b)] --------------------------------------------;性对及推对完 , 公式三:

log(a)(b)=1/log(b)(a)

对明如下:

由对底公式 log(a)(b)=log(b)(b)/log(b)(a) ----取以b对底的对

数,log(b)(b)=1

=1/log(b)(a)

对可对形得:

log(a)(b)*log(b)(a)=1

三角函的和差化对公式数

sinα，sinβ,2sin;α，β,/2?cos;α

β,/2

sinα

sinβ,2cos;α，β,/2?sin;α

β,/2

cosα，cosβ,2cos;α，β,/2?cos;αβ,/2

cosα

cosβ,,2sin;α，β,/2?sin;αβ,/2

三角函的对化和差公式数

sinα ?cosβ,1/2 [sin;α，β,，sin;αβ,]

cosα ?sinβ,1/2 [sin;α，β,,sin;αβ,] cosα ?cosβ,1/2 [cos;α，β,，cos;αβ,] sinα ?sinβ,-1/2 [cos;α，β,,cos;α,β,]