Calculus Answers

FIND THE AREA OF THE REGION ENCLOSED BY THE CURVES X^2=Y AND Y=1/2(X^4+X)

Test the convergence of the series
summation from n=1 to infinity (square root(n^2+1)-n)x^2n ; (x>0)

Test the following series for convergence and divergence :
summation from n=1 to infinity tan^-1(1/n^2+n+1)

Take 10 figure logarithm to bases 10 from x = 300 to x = 310 by unit increment.
Calculate the first derivative of x 10 log when x = 310 .

Find the derivative of the function?
f(x)= (x^3+9x+4)(10+1/x^2)

b) The Fibonacci sequence is defined as follows:

i. List the first eight terms of the sequence.
ii. Find assuming that it exists.

A ball is dropped from a height of 10m. Each time the ball strikes the ground it bounces vertically to a height that is of the preceding height. Find the total distance the ball will travel if it is allowed to bounce indefinitely.

Find the exact value of cos(arcsin(one fourth)). For full credit, explain your reasoning.

Identify the maximum and minimum values of the function y = 8 cos x in the interval [-2π, 2π]. Use your understanding of transformations, not your graphing calculator.