Integral test: Convergence or divergence of a series.

Use the integral test to determine the convergence or divergence of the series: En=1 2 / (3n + 5)

theorem 8.11

Use theorem 8.11 to determine the convergence or divergence of the p-series En=1 3 / (n5/3)

Limit comparison test

Use the limit comparison test to determine the convergence or divergence of the series En=1 2 / (3^n - 5)

Taylor Polynomial

Find the nth Taylor polynomial centered at c f(x)= (x)^1/3 n = 3 c = 8

Power series centered at 0

Use the power series 1 / 1+x = En=0 (-1)^n x^n to determine the power series, centered at 0, for the function h(x) = x / x^2-1 = 1 / 2(1+x) - 1 / 2(1-x)

Interval of convergence

Find the interval of convergence of (a) f(x), (b) f'(x), (c) f''(x), (d) {f(x)dx En=1 [(-1)^n+1 (x-2)^n ] / 2

Basic Derivatives

1.) Find the derivative of the function: a.) f(x) = x + 1/x^2 b.) f(x) = (2/3rd root of x) + 3 cos x 2.) Find equation of tangent line to the graph of f at the indicated point: a.) y = (x^2 + 2x)(x + 1) ; (1,6)

True or False Derivative Questions

True or False and Why? 1.) If f(x) = g(x) + c, then f'(x) = g'(x) 2.) If y = x/pi, then dx/dy = 1/pi 3.) If f(x) = 1/x^n, then f'(x) = 1/(nx^n-1)

Power Series: Interval of Convergence

Find a power series for the function, centered at c, and determine the interval of convergence: f(x)= 4 / 5-x, c=-2

Power series: Interval of Convergence

Determine a power series, centered at 0, for the function, identify the interval of convergence: h(x)= x / x^2-1 = (1 / 2(1+x)) -(1 / 2(1-x))