If the limit is infınity enter "INF", ifthe limit is negative infinity enter "-INF".x+4x-12lim2x→2x2 -4x2 +4x-12lim-2x2 –4x+4x-12lim,→-2+x2 –4x2+4x-12limr→-0x2 -4x2+4x–12limr>00x2 -4x² +x-2limr-→-3x2+4x+3.2x+x-2lim,x→-3+x2 +4x+3x+x-2limr-1x2+4x+3x2 +x-2lim,x→-1+x2+4x+3x2+x-2limgx2+4x+3x2 +x-2limg+00x2+4x+3

Answered: the limit is negative infinity enter…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 60E

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Question

If the limit is infınity enter "INF", if
the limit is negative infinity enter "-INF".
x+4x-12
lim2
x→2
x2 -4
x2 +4x-12
lim-2
x2 –4
x+4x-12
lim,→-2+
x2 –4
x2+4x-12
limr→-0
x2 -4
x2+4x–12
limr>00
x2 -4
x² +x-2
limr-→-3
x2+4x+3
.2
x+x-2
lim,
x→-3+
x2 +4x+3
x+x-2
limr-1
x2
+4x+3
x2 +x-2
lim,
x→-1+
x2+4x+3
x2+x-2
limg
x2+4x+3
x2 +x-2
limg+00
x2+4x+3

Expert Solution

Step 1

Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and specify the other subparts (up to 3) you’d like answered

Step 2

Given: Expression of the limit as

$\lim_{x \to 2} \frac{x^{2} + 4 x - 12}{x^{2} - 4}$
$\lim_{x \to - 2^{-}} \frac{x^{2} + 4 x - 12}{x^{2} - 4}$
$\lim_{x \to - 2^{+}} \frac{x^{2} + 4 x - 12}{x^{2} - 4}$

To find: The value of limit in each expression.

Step 3

Explanation:

Solving $\lim_{x \to 2} \frac{x^{2} + 4 x - 12}{x^{2} - 4}$ ,

$\lim_{x \to 2} \frac{x^{2} + 4 x - 12}{x^{2} - 4} = \lim_{x \to 2} \frac{x^{2} + 6 x - 2 x - 12}{x^{2} - 2^{2}} [factorising the numerator and denominator] = \lim_{x \to 2} \frac{x (x + 6) - 2 (x + 6)}{(x + 2) (x - 2)} = \lim_{x \to 2} \frac{(x + 6) (x - 2)}{(x + 2) (x - 2)} [cancelling (x - 2) from nimerator and denominator] = \lim_{x \to 2} \frac{(x + 6)}{(x + 2)} = \frac{2 + 6}{2 + 2} = \frac{8}{4} = 2$

Answer: $\lim_{x \to 2} \frac{x^{2} + 4 x - 12}{x^{2} - 4} = 2$ .

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