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Chapter 12: Q 15 (page 975)

Show that the minimal value of

Short Answer

Expert verified

Minimal value is

Step by step solution

01

Step 1. Given Information

We have given the following function

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Most popular questions from this chapter

Use Theorem 12.32 to find the indicated derivatives in Exercises 21–26. Express your answers as functions of a single variable.

dzdtwhenz=x3ey,x=sint,andy=cost

Use Theorem 12.33 to find the indicated derivatives in Exercises 27–30. Express your answers as functions of two variables.

∂z∂twhenz=x2y3,x=tsins,andy=scost

Achainruleforfunctionsoftwovariables:Letf(x,y)=x2y3,x=scost,andy=ssint.Find∂x∂sand∂x∂t.

Describe the meanings of each of the following mathematical expressions :

fyx0,y0

Letz=f(x,y)g(x,y).Showthat∂z∂x=∂f∂xg(x,y)+f(x,y)∂g∂xand∂z∂y=∂f∂yg(x,y)+f(x,y)∂g∂y
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