Reference no: EM131015629
1. Consider the following.
f(x) = 1 / (1 + x)
Find the Taylor series at x = 0 of the given function. Use suitable operations (differentiation, substitution, etc.) on the Taylor series at x = 0 of 1/(1 - x). For reference: This series is derived in your textbook. (To be graded as correct, give your answer up to and including the x4 term. Answers with more or less terms will be graded as incorrect.)
2. Consider the following.
f(x) = x / (1 - x)3
Find the Taylor series at x = 0 of the given function. Use suitable operations (differentiation, substitution, etc.) on the Taylor series at x = 0 of 1/(1 - x). For reference: This series is derived in your textbook. (To be graded as correct, give your answer up to and including the x4 term. Answers with more or less terms will be graded as incorrect.)
3. Consider the following.
∫1 / (1 + x3) dx
Find the Taylor series expansion at x = 0 of the given antiderivative. (To be graded as correct, give your answer up to and including the x10 term. Answers with more or less terms will be graded as incorrect.)
4. Consider the following.
∫ x ex^3 dx
Find the Taylor series expansion at x = 0 of the given antiderivative. (To be graded as correct, give your answer up to and including the x11 term. Answers with more or less terms will be graded as incorrect.)
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