高数(理工类-第四版)上册复习练习题答案(3)

又 f(0) f(0) f(0)　．得f(0) 0 lim

f( x) x

lim

f( x) f(0)

x

f (0) 1

x 0 x 0

f (x) 1 2x

lim

f(cosx) f(1)

x

1

2

x 0

lim

x 0

f 1 (cosx 1) f(1)cosx 1

2

cosx 1x

f (1) 2 f (1) 4

2

10设函数x x(y)由方程yx x y 4确定,求dx

dx

x (1)dy

y 1

y 1

　　　 3dy

11求由方程ysinx cos(x y) 0

确定的隐函数y的微分dy.

得　dy

ycosx sin(x y)sinx sin(x y)

dx

解法2　dy yx dx

ycosx sin(x y)sinx sin(x y)

dx

dy x t 2t

12设　y limt ，x e 1，求 2

x x tdx

y limt(1

x

x

2

2tx t

)

x

te

2t

dydx

2

e(1 2t)2ed(

2t

2t

121

t

dy

dydx

2

dx dx

)d(

dt

t)

/

dxdt

t2e

2t

13设　y lncos(tan3x) chx cot(x 1)，求y (x)．

2