Question

Please answer all, be explanatory but concise. Thanks.

Consider the function f(x) = e x a. Differentiate the Taylor series about 0 of f(x). b. ldentify the function represented by the differentiated series c. Give the interval of convergence of the power series for the derivative. Consider the differential equation y'(t) - 4y(t)- 8, y(0)4. a. Find a power series for the solution of the differential equation b. ldentify the function represented by the power series. Use a series to estimate the following integral's value with an error of magnitude less than 10 8 0.3 2 0 0.3 2 Use a Taylor series to approximate the following definite integral. Retain as many terms as needed to ensure the error is less than 10-4 0.1 1x dx 0.1 ./ 1 + x5 dx (Round to four decimal places as needed.) 0 () 5 Use an appropriate Taylor series to find the first four nonzero terms of an infinite series that is equal to In Write the first four nonzero terms for the series in order. Simplify your answers.) Use Taylor series to evaluate the following limit. Express the result in terms of the parameter. ax lim x→0 ax lim X-0 Teams A and Β go into sudden death overtime after playing to a when it has the ball, with Team A having the ball first. e. The teams a e ate possession ofthe ball and the st team to score wins. Each team asa i chance scoring 2 (312k Σ a. The probability that Team A ultimately wins is Evaluate this series. b. The expected number of rounds (possessions by either team) required for the overtime to end is k k-1 2 (3 (Simplify your answer.)

Answer 1

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