Fill in the blanks first 1, and the function value f (- 1) = 0.

2,x→0,lim( 1-x)^(2/x)= 1

3，∫[ 1/√(x？ +a？ )]dx=in[x+√(x？ +a？ )]+C

Second, multiple-choice questions 4, (A) 1, 5, (A) 1/[√(x? + 1)? ]

6,

Three, seven, x→ 0, lim [ln( 1+2x? )]( 1-cos x)=[2x/( 1+2x？ )] / sin x=2x/[( 1+2x？ ) sin x]

8. Find the function y= x? Tangent Equation at M0 (2 2,8)

The tangent point is n (- 1,-1), and the tangent equation is y=3x+2.

9 . y′= dy/dx =-cos[2x/( 1+x)？ ]? [2x/( 1+x)？ ]′

[2x/( 1+x)？ ]' =[2( 1+x)？ -4x( 1+x)]/( 1+x)^4=2( 1-x)/( 1+x)？

∴dy/dx=-cos[2x/( 1+x)？ ]? [2( 1-x)/( 1+x)？ ]

dy =-cos[2x/( 1+x)？ ]? [2( 1-x)/( 1+x)？ ]dx

10 Find the minimum value of the function y = 2x/ln x.

If the derivative is equal to 0, y'=[2 LNX-2x/x]/(LNX)? =0

Ln x= 1, x= e, replaced by y=2x/ln x,

Minimum y=2e

Four, 12. Find the function y= sin? Derivative of 100 x

Y'=2cos x, y "=-2sinx, the third derivative of y =-2cosx, and the fourth derivative of y "=-2 sinx;

The fifth derivative of y =2cos x, and then loop,

∴ Function y= sin? 65438+x = 000th derivative of 2sinx

14，∫{[√(x？ -4)]/ x} dx=∫(x？ -4)-2 arc cos(2/| x |)+C