Calculus Answers

Let A denote the area of the graph of f(x)=rootx on [0, 1] and let B denote the area of the graph of f(x)=x^2 on [0, 1]. Explain geometrically why A+B=1

Derive the following reduction formula :
Integral x^n e^x dx=x^n e^x-n integral x^n-1 e^x dx

Trace the curve y=2x^2-8/x^2-16 by showing all the properties used to trace the curve.

Obtain the largest possible domain, and corresponding range, of the function f, defind by f(x)=x-2/3-x

Evaluvate integral 0 to 1 tan inverse xdx.

Let f(x)={x^2-16x, x<9;12rootx, x> or equal to 9.Is f continuous at x=9? Determine whether f is differentiable at x=9.If so, find the value of the derivative there.

Find the slope of the curve y^2-x+1=0 at the points (2, -1) and (2, 1).

Find dy/dx if 2y^3t+t^3y=1 and dt/dx=1/cost

Prove that cos x graterthan or equal to 1(-x^2/2)for all x in the interval [0, 2pi]

Find the equation of the tangent lines at all inflection points of the graph of
f(x)=x^4-6x^3+12x^3-8x+3.