The equation for the length of a hypotenuse of a right triangle

| August 31, 2017

Question

Problems 1-6 are each worth 15 points. Problem 7 is worth 10 points. Please show all work. Failure to show intermediate steps will result in zero credit.

1. The equation for the length of a hypotenuse of a right triangle is given by the function z below. Please show all intermediate steps.

a) Find the total differential equation for z

b) Determine the value of the total differential (dz) when x = 6, y = 8, dx = 0.25 and

dy = -0.125 (all values are in inches)

c) Interpret your answer from question b.

2. Use calculus to sketch the following equation. Use the second derivative test to determine whether a stationary point is a maximum, minimum or inflection point. Please show all intermediate steps.

3. Find dz/dt given the following information. Please show all intermediate steps.

4. Find all local stationary points. Determine whether each point is a maximum, minimum or a saddle point. Please show all intermediate steps.

5. Use the Lagrange multiplier method to find stationary points for the following problem. Evaluate the second order conditions. Please show all intermediate steps.

6. Evaluate the following indefinite integral. Please show all intermediate steps.

7. Evaluate the following definite integral. Please show all intermediate steps.

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