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Question: Use a known Taylor series to conjecture the value of the limit. \(\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin {{x}^{2}}-{{x}^{2}}}{{{x}^{6}}}\) Solution: The solution consists of 54 words (1 page)Deliverables: Word Document

Question: Use cylindrical shells to compute the volume of the region bounded by \(x={{y}^{2}}\) and x = 4, revolved about y = 2. Solution: The solution consists of 56 words…

Question: A rectangular box with an open top is to have a volume of 10 cubic feet. The length of the base is twice its width. Material for the base…

Question: Calculate \(\int\limits_{\frac{\sqrt{3}}{2}+1}^{2}{\sqrt{2x-{{x}^{2}}}dx}\) Solution: The solution consists of 103 words (2 pages)Deliverables: Word Document

Question: Find the area under the curve given by the function \[f(x)={{x}^{3}}+{{x}^{2}}-1\] on the interval \[[-2,1]\] Solution: The solution consists of 106 words (1 page)Deliverables: Word Document

Question: Indicate whether each of the series given below is convergent or divergent. Identify the test you apply to support your conclusion a- \(\sum\limits_{n=1}^{\infty }{\frac{{{\tan }^{-1}}n}{{{n}^{2}}}}\) b- \(\sum\limits_{n=1}^{\infty }{\frac{1}{\sqrt{8{{n}^{2}}-3n}}}\) c-…

Question: Find the derivative of the function \[f(x)=\sqrt{x+1}\left( {{e}^{3}} \right)\]. Solution: The solution consists of 23 words (1 page)Deliverables: Word Document

Question: Sketch a curve that satisfies: , and . What is ? Solution: The solution consists of 42 words (1 page)Deliverables: Word Document

Question: Same question for the function \(g:{{\mathbb{R}}^{2}}\to \mathbb{R}\) defined by \[g\left( \theta ,\phi \right)=\left( \sin \theta \cos \phi ,\sin \theta \sin \phi ,\cos \theta \right)\] Solution: The solution consists of…

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