Critical Points and Extrema

Find the critical points and test for relative extrema: f(x,y)= x^3 - 3xy + y^3

Taylor Polynomial

find the Taylor polynomial of degree 4 at c=1 for the equation f(x)=ln x and determine the accuracy of this polynomial at x=2.

Determine all points x at which f is differentiable.

Let f(x) = { x|x| if x is rational 0 if x is irrational determine all points x at which f is differentiable.

Find all differentiable functions.

Find all differentiable functions f : R ---> R such that (f composed f) = f. R = All Real Numbers (f composed f) = the function f composed with itself

Convergence or divergence, absolute or conditional

Sigma infinity above and n=2 below times (1/(n*ln^2*n).

Functions: Limits

what is lim (sin x) / (1-cos x) as x approaches 0?

Partial derivatives

Find partial derivatives dw/ds, and dw/dt where (d substitued for symbol, my equation writer seems not to be working) w=x^2-y^2 x=cos t y=s sin t s=3 t= Pi/4

Convergence or Divergence

Test for convergence or divergence, absolute or conditional. If series converges and it is possible to find the sum, then do so. SUM n=1 of 2n+1 / n^2 +2

Series Convergence: Two-sided Estimator

Please see the attached file for the fully formatted problems. A simple technique to estimate values of the finite sums of reciprocals to natural numbers raised to positive power and to define if corresponding infinite series converge. Deduce two-sided estimator for the sums of the positive powers (p) of reciprocals to nat ...continues

Find the partial derivatives

Find partial derivatives for w/s and w/t where: w=x^2-y^2, x=cos t, y=s sin t, s=3, t=pie/4