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1. Consider the following.
f(x) = x3ex^2
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 ex.2. Consider the following Taylor series expansion.
1/√(1+x) = 1 - (1/2)x + (1·3/2·4)x2 - (1·3·5/2·4·6)x3 + (1·3·5·7/2·4·6·8)x4 -...
Find the Taylor series of the following at x = 0. (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.)
f(x) = 1/√(1-x)
3. Consider the following Taylor series expansion.
Find the Taylor series of the following at x = 0. (To be graded as correct, give your answer up to and including the x8 term. Answers with more or less terms will be graded as incorrect.)
f(x) = 1/√(1-x2)
Solve by absolute value equation and Solve by factoring and use the zero product principle.
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