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Question: Solve the following integral \[\int{\frac{x-1}{{{x}^{2}}-4x-5}dx}\] Solution: The solution consists of 96 words (2 pages)Deliverables: Word Document

Question: The height h in feet of an object after t seconds is given by the function h = –16t2 + 60t + 6. How long will it take the…

Question: Given \(f\left( x,y \right)=\ln \sqrt{{{x}^{2}}+{{y}^{2}}}\), find (a) The direction and maximum rate of increase of \(f\left( x,y \right)\) at (1, 2). (b) The directional derivative of \(f\left( x,y \right)\)…

Question: Find the centroid of the solid region of uniform density between the xy-plane and the paraboloid \[z=4-\left( {{x}^{2}}+{{y}^{2}} \right)\] Solution: The solution consists of 76 words (2 pages)Deliverables: Word…

Question: Using spherical coordinates find the volume of the solid bounded below by the cone \({{x}^{2}}+{{y}^{2}}=3{{z}^{2}}\), and the above sphere \({{x}^{2}}+{{y}^{2}}+{{z}^{2}}=4\) Solution: The solution consists of 95 words (2 pages)Deliverables:…

Question: Determine the absolute minimum and maximum of \(y=\frac{{{x}^{2}}+4}{x}\). on the interval [1, 5]. Solution: The solution consists of 130 words (1 page)Deliverables: Word Document

Question: Find the absolute maximum and minimum values of \(h(x)=x+\frac{9}{x}+2\) on the interval [1,10]. Solution: The solution consists of 86 words (1 page)Deliverables: Word Document

Question: Solve the following Cauchy-Euler equation \[{{x}^{2}}y''+2xy'-2y=2-\ln \left( {{x}^{4}} \right)\] Solution: The solution consists of 202 words (3 pages)Deliverables: Word Document

Question: Find both first partial derivatives \[z=\ln \sqrt{xy}\] Solution: The solution consists of 23 words (1 page)Deliverables: Word Document

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