Interval and radius of convergence
Not what you're looking for?
Please see the attached image for complete questions.
1. Find the interval of convergence (including a check of end-points) for each of the given power series.
2. Use the geometric series test (GST) to write each of the given functions as a power series centred at x=a, and state for what values of x the series converges.
3. Use known Maclaurin series for e^x, 1/(1-x), and sin(x) to derive Maclaurin series for the given functions. State the operations used, and the radius of convergence of the series derived.
4. In problem 3, the radius of convergence was known from theorems involving the various operations. In this problem, complete the determination of the interval of convergence by checking the end-points of each of the series found in problem 3.
5. Find the specified Taylor polynomial P_N(x) centered at x=a for each of the given functions by evaluating f, f', f'', ... at x=a to determine the coefficients.
Purchase this Solution
Solution Summary
This solution shows all the steps to solve the given questions regarding the interval and radius of convergence.
Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Probability Quiz
Some questions on probability