Integral evaluation

Please see the attached file for full problem description.

Series Test

Test the series (in the attached file) for convergence or divergence by using the Comparison Test or the Limit Comparison Test.

Convergence/Divergence Test

Using the Comparison Test or the Limit Comparison Test, test the series in the attached file 'Question.doc' for convergence or divergence.

Volume Using Cylindrical Shells

See attached Word file.

Implicit Differentiation

An function y=f(x) is defined implicitly by the formula x=tan(y), with the condition y epsilon (-pi/2, pi/2). Find and formula for its derivative, then obtain the formula for f'(x) in term of x alone.

limit

lim (x^3)/(e^x) X->∞

Limit Calculation

lim X^(1/x) X->∞

limit

lim (x+1)^(1/X) X->0

limit

lim (x-1)*ln(x) x->1

Finding the limit of a function using L'hopital rule

Find lim (ln x)^3/(x) as x--> infinity