Chapter 10, Problem 58RE

Find the radius of convergence, R, of the series. R = 8 I = n = 1 n²x^ 3 6 9 (3n) Find the interval, I, of convergence of the series. (Enter your answer using interval notation.

The function f(x) = ekx² can be expressed in power series form. If A is the approximate value of f(x) at x = 0.767 when the series is truncated to five terms and B is the approximate value of f(x) at x = 0.767 when the series is truncated to four terms, what is the absolute error between A and B given that k = 3? Round off the final answer to five decimal places but do not round off on preliminary calculations.

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

The question is to find a power series for the function centered at c f(x) = 5/(5-x) , c = -3

Find first two terms of the Taylor 3 d) ( series centered at a = 2 of the function f(x) x+ 2

be the first three terms of the binomial series to approximate f(x) = 1 at x = 1/2. Then find f(¹/2) √1-X using a How clase was your approximation? calculater.

Find the series' interval of convergence and, within its interval, the sum of the series as a function of ?x.

Find the smallest number of terms of the series Σ (-1)² = 3/ k k = 1 we need to add in order to estimate the sum of the series with error less than 8/58.

An individual is given a dose of Q units of a certain drug. the amount that remains in the bloodstream at the end of t minutes and Qe−ct, with c > 0. Suppose that the same dose is administered at successive intervals of T minutes. (a) Using series, express the amount A(k) of the drug in the bloodstream immediately after the K-th dose.(b) Find an upper bound for the amount of drug in the bloodstream after an arbitrary number of doses.(c) Find the shortest time between doses that ensures that A(k) does not exceed a certain level M, M > Q.