Calculus Answers

Find the nature of the roots of the polynomial
2X5+ X³+ 5X+ 1

Integrate (7x+8)/(2x²+11x+5)dx
Integrate (3x²+18x+3)/(3x²+5x-2)dx
Integrate (6x²)/(x²-4)dx
Integrate (sin inverse x) /(x²-4)dx
Integrate (x²+1)³/(x+2)dx

Trace the curve Y=(2x²-8)/(x²-16) by showing all the properties used to trace the curve.

The area of a square with side s is A(s)=s². What is the rate of change of the area of a square with respect to its side length when s=8?

Find d²y/dx² for y=csc(x)

Using the sequential definition of continuity, prove that the function f: R → R ,
defined by f(x) = 3x^2+ 7 ,∀x ∈R,
is continuous.

Test the conditional convergence of the series


1-1/root2+1/root3-1/root4+....

Justify that


lim 1/(5-x)^2
x tend to5 = ∞

Evaluate

3n
Lim ∑ rootn/(n+3r)^3/2
n→∞ r=0

Check whether the following sequences are convergent:

1){4+(-1)^n}

2){(4n+n^2)/(2n^2+3n)}