Exam 3 (MTH 251)-Fall 2022
美国数学代考 Find a power series representation for the following functions. Determine the radius of convergence for each series you obtain.
Exam 3 will be on Nov. 18, covers sections 11.5-11.11, and will be given during our regular class. I strongly recommend to review my notes and examples we discussed during our meetings. I will hold a review session for the exam on Wednesday (Nov. 16) during our regular class. You are allowed to use a scientifific calculator on this exam. The use of graphing calculators or calculators with symbolic manipulation capabilities is not allowed. Below are some problems to practice, taken from my old exams for this course. We will discuss some of these problems during the review session.
1.Determine whether each series is absolutely converges, conditionally convergent or divergent. Explain your reasoning clearly and state which test you use in each case. 美国数学代考
2.Find the interval of convergence of the following series:
3.Find a power series representation for the following functions. Determine the radius of convergence for each series you obtain.
4.Approximate each defifinite integral to six decimal places.
5.How many terms of the series 美国数学代考
do we need to add in order to fifind the sum with error less than 0.001.
6.Find the Taylor series of each function at the given point:
(a) f(x) = 
at a = 16.
(b) f(x) = cos x at a = π/2.
(c) sin(2x) at a = 
7.Consider the function f(x) =e x 2.
(a) Find T3(x), the second degree Taylor polynomial of f at a = 0.
(b) Estimate the accuracy of the approximation f(x) ≈ T3(x) when 0 ≤ x ≤ 0.1.
8.Estimate the range of values of x for which the approximation
is accurate with |error| < 0.01.
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