Find the indicated limit by using the limits lim(r, у) (а, b)f(x, y) = 4 andlim(х, у) (а, b)g(x, y) = -5. lim [f(x, y)g(x, y)](х, у) (а, b)- y)

Answered: lim (r, у) (а, b) f(x, y) = 4 and lim…

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lim (r, у) (а, b) f(x, y) = 4 and lim (х, у) (а, b) g(x, y) = -5. lim [f(x, y)g(x, y)] (х, у) (а, b) - y)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.3: Algebraic Expressions

Problem 20E

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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

Find the indicated limit by using the limits

lim
(r, у) (а, b)
f(x, y) = 4 and
lim
(х, у) (а, b)
g(x, y) = -5.

Expert Solution

Step 1

Given: $\lim_{(x, y) (a, b)} f (x, y) = 4$ and $\lim_{(x, y) (a, b)} g (x, y) = - 5$ .

To evaluate: $\lim_{(x, y) (a, b)} [f (x, y) g (x, y)]$ .

Solution:

Product rule of limit states that:

$\lim_{x \to a} [f (x) g (x)] = \lim_{x \to a} f (x) \cdot \lim_{x \to a} g (x)$

Using above property, we will evaluate the limit.

$\begin{array}{rcl} \lim_{(x, y) \to (a, b)} [f (x, y) g (x, y)] & = & \lim_{(x, y) \to (a, b)} f (x, y) \cdot \lim_{(x, y) \to (a, b)} g (x, y) \\ = & 4 \cdot (- 5) \\ = & - 20 \end{array}$

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$Limits and Continuity$

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