Chapter 12: Q. 5 (page 989)

Evaluate the following limits, or explain why the limit does not exist.
$\lim_{(x, y) \to (1, 2)} \frac{x^{2} + y^{2}}{x^{2} - y^{2}}$

Short Answer

Expert verified

$\lim_{(x, y) \to (1, 2)} \frac{x^{2} + y^{2}}{x^{2} - y^{2}} = \frac{- 5}{3}$

Step by step solution

Step 1. Given information is:

$\lim_{(x, y) \to (1, 2)} \frac{x^{2} + y^{2}}{x^{2} - y^{2}}$

Step 2. Evaluating Limits

$Since as (x, y) \to (1, 2), x^{2} + y^{2} = 1^{2} + 2^{2} = 5, x^{2} - y^{2} = 1^{2} - 2^{2} = - 3 \lim_{(x, y) \to (1, 2)} \frac{x^{2} + y^{2}}{x^{2} - y^{2}} = \frac{5}{- 3} = - \frac{5}{3} Hence, \lim_{(x, y) \to (1, 2)} \frac{x^{2} + y^{2}}{x^{2} - y^{2}} = \frac{- 5}{3}$

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Evaluate the following limits, or explain why the limit does not exist.
$\lim_{(x, y) \to (1, 2)} \frac{x^{2} + y^{2}}{x^{2} - y^{2}}$

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Evaluating Limits

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Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Evaluating Limits

One App. One Place for Learning.

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Evaluate the following limits, or explain why the limit does not exist.
$\lim_{(x, y) \to (1, 2)} \frac{x^{2} + y^{2}}{x^{2} - y^{2}}$