question B The image contains the following mathematical limits:(a) $\lim_{{x \to 1}} \frac{{x^2 - 4}}{{x + 2}}$(b) $\lim_{{x \to -2}} \frac{{x^2 - 4}}{{x + 2}}$These expressions represent limits of rational functions as $x$ approaches specific values. The expression $\frac{{x^2 - 4}}{{x + 2}}$ involves a quadratic polynomial in the numerator and a linear polynomial in the denominator. Key steps in solving such limits typically involve simplifying the expression, often by factoring the numerator, and then evaluating the limit.

Name: question B The image contains the following mathematical limits:(a) $
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Description: question B The image contains the following mathematical limits:(a) \(\lim_{{x \to 1}} \frac{{x^2 - 4}}{{x + 2}}$(b) $\lim_{{x \to -2}} \frac{{x^2 - 4}}{{x + 2}}$These expressions represent limits of rational functions as $x$ approaches specific

We have to evaluate the limit: blimx→-2x2-4x+2 After putting limit value we get that it is in the…

Answered: x²-4 (b) lim 4-2 X+2

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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question B

The image contains the following mathematical limits:

(a) $\lim_{{x \to 1}} \frac{{x^2 - 4}}{{x + 2}}$

(b) $\lim_{{x \to -2}} \frac{{x^2 - 4}}{{x + 2}}$

These expressions represent limits of rational functions as $x$ approaches specific values. The expression $\frac{{x^2 - 4}}{{x + 2}}$ involves a quadratic polynomial in the numerator and a linear polynomial in the denominator. Key steps in solving such limits typically involve simplifying the expression, often by factoring the numerator, and then evaluating the limit.

Expert Solution

Step 1

We have to evaluate the limit:

$(b) \lim_{x \to - 2} \frac{x^{2} - 4}{x + 2}$

After putting limit value we get that it is in the form of $\frac{0}{0}$ .

We can use factoring law to evaluate the limit

here in numerator we can use the identity $a^{2} - b^{2} = (a - b) (a + b)$

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