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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)
A company wishes to manufacture a box with a volume of 48 cubic feet that is open on top and is twice as long as it is wide. Find the width of the box that can be produced using the minimum amount of material.
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Law of sines.
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