Calculus Answers

Prove that for every
x>0, x/(1+x^2)<tan^-1x<x

Differentiate tan^-1{(sinx-cosx)/(sinx+cosx)} with respect to x/2

If f(x)=(4x^2-7x-2)/(x-2), x not is equal to 0
Find a delta > 0 such that
|f(x)-9|< 1/100 for 0<|x-2|<delta.
Hence show that lim x->2 f(x)=9

Find the area enclosed by the curve r = a(1-cos theta) with detail explanation

Prove that
Integration of (√cos^n x dx)/(√cos^n x + √sin^n x )within limit 0 to π/2=π/4

If x sin y=sin(p+y), p belongs to R
show that sin p dy/dx+ sin^2 y=0

Given an example of a function which is not integrable on [0, π].Justify your answer.

Find the volume of the solid obtained by revolving the curve
x=a cos^3 theta
y=a sin^3 theta
about the y-axis.

d/dx[integration of sin(t^2)dt within limit x^2 to 0]= -sin(x^2)
Is the statement true or false? Give reason in support of your answer.

Rolle’s theorem is applicable for the function f, defined by f(x)=1+x^(2/3) in the
interval [-1,1].
Is the statement true or false? Give reason in support of your answers.