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Find the particular solution for the initial value problem. = ; y(e) = 8

Use the total differential to approximate the quantity. Then use a calculator to approximate the quantity, and give the absolute value of the difference of the two results to four decimal places.0.97e0.02

Find the partial derivative.Let z = f(x,y) = 5×2 – 18xy + 4y3. Find .

Solve the problem.The total cost to hand-produce x large dolls and y small dolls is given by If a total of 40 dolls must be made, how should production be allocated so that the total cost is minimized?

Find the second-order partial derivative.Find fxx when f(x,y) = 8x3y – 7y2 + 2x.

Evaluate dz.z = x3 – 9xy2 + 5y; x = 3, y = 3, dx = 0.01, dy = -0.03

Choose the graph that matches the equation.z = -x2 – y2

Describe in a few complete sentences how to test that the width value you found will indeed be the width that will minimize the total area.

A graphic artist is designing a rectangular poster with margins of 2 inches at the top and along each side, and a 3-inch margin at the bottom. To minimize costs, she wants to keep the total area of the poster as small as possible while ensuring that the printed area (the part inside the margins) is exactly 180 in². Let w represent the width of the printed area and h the height of the printed area. What are the overall dimensions of the poster?

Using your loose-leaf paper, simplify the area by distributing the terms and enter the simplified and expanded total area function.