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