Power Series Representation

I am trying to figure out a powers series representation for the function f(x) = e^x, centered at c = -2. I also need to find the interval of convergence.

power series

I am trying to find the interval of convergence for the attached power series (attached as a gif). I am also supposed to check the endpoints for convergence. I'm not that good with power series and the format of this power series is really throwing me off. So I am looking for the steps to find the interval of convergence (also c ...continues

Implicit Differentiation

Find y" for x^2/a^2 - y^2/b^2 = 1

Extending power series.

Extend e^(x) into a power series at center x=1

Expansion of a function using Taylor's Theorem

Use Taylor's Theorem to expand the function 2(x^5) + x^2 - 3x - 5 in powers of x+1.

Double Integration

Evaluate the double integral Transform the double integral of (i) using plane polar coordinates Show that the 3 x 3 determinant See attached file:

Arc length of the curve defined by a parametric system

Find arc length of the curve defined by the following parametric system: x=cos^-1(t) (inverse cosine) y= ln t where t is less than/equal to 1, greater than/equal to (1/sqrt 2)

Applied Max-Min Problems

Please show as much work as possible, so I can understand how to solve these problems on my own. Thank you. 1. A printing company has eight presses, each of which can print 3600 copies per hour. It costs $5.00 to set up each press for a run and 10+6n dollars to run n presses for 1 hour. How many presses should be used to pr ...continues

Working with growth and decay rates and evaluating decay rate expressions.

A crude-oil refinery has an underground storage tank which has a fixed volume of 'V' liters. Due to pollutants, it gets contaminated with 'P(t)' kilograms of chemical waste at time 't' which is evenly distributed throughout the tank. Oil containing a variety of pollutants with concentration of 'k' kilograms per liter enters ...continues

Maclaurin series

Use the Maclaurin series for sinx and cosx to show that sin2x=2sinxcosx