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Question: If $3000 is invested in an account that pays interest compounded continuously, how long will it take to grow to $6000 at 7%? Solution: The solution consists of 58…

Question: Labeling the axes and intercepts, etc. make a neat sketch and name each of the following surfaces. (a) \({{x}^{2}}+2{{y}^{2}}=4\) (b) \({{x}^{2}}+2{{y}^{2}}=z\) (c) \({{x}^{2}}+{{y}^{2}}-4{{z}^{2}}=4\) Solution: The solution consists of 62…

Question: (a) Sketch the area bounded by the top half of the disc \({{\left( x-1 \right)}^{2}}+{{y}^{2}}=1\) (b) Evaluate \[\iint\limits_{D}{\frac{1}{\sqrt{{{x}^{2}}+{{y}^{2}}}}dA}\] Solution: The solution consists of 78 words (2 pages)Deliverables: Word Document

Question: Compute the divergence and the curl of the vector function: \[\vec{F}\left( \mathbf{x} \right)=\left( {{x}^{2}}+{{y}^{2}}-xyz,x{{z}^{2}}\cos y,{{z}^{2}}{{e}^{{{x}^{2}}+{{y}^{2}}}} \right)\] Solution: The solution consists of 79 words (1 page)Deliverables: Word Document

Question: A constant force F (1,-1, 5) acts through a point (-1, 3,-1). Find the resulting torque around the point (2, 3, 0). Solution: The solution consists of 69 words…

Question: Find the first, second and third derivatives of \(f\left( x \right)=3{{x}^{4}}+12\sqrt{x}-\frac{5}{{{x}^{2}}}\) Solution: The solution consists of 27 words (1 page)Deliverables: Word Document

Question: Find the antiderivative of the following functions (a) \(\int{\left( {{e}^{x}}-2{{\csc }^{2}}x-\pi \right)dx}\) (b) \(\int{\frac{{{x}^{5}}-3x+1}{{{x}^{2}}}}dx\) (c) \(\int{5{{x}^{4}}{{\left( 2-4{{x}^{5}} \right)}^{1/3}}dx}\) (d) \(\int{\left( \frac{\cos x-\sin x}{\cos x+\sin x} \right)dx}\) Solution: The solution…

Question: For the function given above, supply the following information: \[f(x)=\frac{{{x}^{3}}-1}{{{x}^{3}}+1}\] \[{f}''(x)=\] Solution: The solution consists of 49 words (1 page)Deliverables: Word Document

Question: The centripetal acceleration of a particle moving in a circle is \(a=\frac{{{v}^{2}}}{r}\), where v is the velocity and r is the radius. Approximate the maximum percent error in measuring…

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