Calculus Answers

show that x-(x^2/2)<ln(1+x)<x-{x^2/2(1+x)} domain x>0.

if y to the base n = ∫ (sin nx/sin x)dx , then show that y = [2 sin(n-1)x/(n-1)]+y to the base n-2 , hence evaluate ∫ upper limit pi/2,and lower limit 0 (sin7x/sin x)dx.

evaluate the integral ∫ dx/ square root of the (x-a)(b-x) , b>a

evaluate the integral ∫ dx/square root of (4+8x-5x^2)

evaluate the integral ∫ dx/(3+4x^2)(square root of (4-3x^2)

evaluate the integral ∫ dx/1+cos x

Trace the following curves. Give all the properties that are necessary for doing so. (1) y^2 = (x-1)(x-2)(x-3) , (2) y^2(x-2) = x^2 (x+a);a>0

if cos^-1(y/b)=log(x/n)^n , then show that x^2 y tto the base n+2 +(2n+1)x y to the base n+1 +2n^2 y to the base of n = 0

find the n^th derivative of x/x^2 +a^2 .

If& f(x)=(1/x)[sup]x[/sup] , find f ``(1).