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Chapter 12: Q 13 (page 975)

Show that the unique solution of the system of equations

Short Answer

Expert verified

The unique solution is

Step by step solution

Step 1. Given Information

We have given the following system of equations

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Most popular questions from this chapter

Find the gradient of the given function, and find the direction in which the function increases most rapidly at the specified point P.

$f (x, y) = \tan^{- 1} (\frac{y}{x}), P = (- 2, 2)$

$Let z = f (x, y) g (x, y) . Show that \frac{\partial z}{\partial x} = \frac{f_{x} (x, y) g (x, y) - f (x, y) g_{x} (x, y)}{(g {(x, y))}^{2}} and \frac{\partial z}{\partial y} = \frac{f_{y} (x, y) g (x, y) - f (x, y) g_{y} (x, y)}{(g {(x, y))}^{2}}$

In Exercises, find the maximum and minimum of the function f subject to the given constraint. In each case explain why the maximum and minimum must both exist.

$f (x, y) = x + y$ when $x^{2} + y^{2} = 16$

Prove that if you minimize the square of the distance from the origin to a point (x, y) subject to the constraint $g (x, y) = 0$ , you have minimized the distance from the origin to (x, y) subject to the same constraint.

Fill in the blanks to complete the limit rules. You may assume that $lim_{x \to a} f (x)$ and $lim_{x \to a} g (x)$ exists and that k is a scalar.

$lim_{x \to a} k f (x) =$

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Show that the unique solution of the system of equations

Short Answer

Step by step solution

Step 1. Given Information

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Most popular questions from this chapter

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