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Question: Find the volume of the “ice cream cone” bounded by the sphere \({{x}^{2}}+{{y}^{2}}+{{z}^{2}}=1\), and the cone \(z=\sqrt{{{x}^{2}}+{{y}^{2}}-1}\). Solution: The solution consists of 73 words (1 page)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: Sketch the graph of \(f\left( x \right)=x+6\). Solution: The solution consists of 12 words (1 page)Deliverables: Word Document

Question: A young couple receives an inheritance and decides to put some of it away in a college fund for their 1-year old daughter. They decide that they will need…

Question: Problem 5. Calculate the derivative of the function from the definition only, using limits. Show your work. \[f(x)=\frac{1}{x+1}\] Solution: The solution consists of 64 words (1 page)Deliverables: Word Document

Question: A spherical weather balloon 3 m in radius is covered with a uniform layer of ice 1.8 mm thick. Use differentials to approximate the volume of the ice. Recall…

Question: Use L’Hospital Rule to find \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{e}^{x}}-1}{x}\] Solution: The solution consists of 24 words (1 page)Deliverables: Word Document

Question: The rate of change in the temperature T of coffee at time t is proportional to the difference between the temperature M of the air at time t and…

Question: Solve the given third-order initial value problem using the method of Laplace transforms: \[\begin{align} & y'''+4y''+y'-6y=-12; \\ & y\left( 0 \right)=-4,\,\,y'\left( 0 \right)=4,\,\,y''\left( 0 \right)=-2 \\ \end{align}\] Solution: The…

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