Answered: x-4x- 12 x - 4x-12 Explain why lim =… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 7E

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Question

X-4x- 12
X-4x-12
Explain why lim
= lim (x+2), and then evaluate lim
X-6
X-6
X6
X-6
...
Choose the correct answer below.
O A.
X-4x- 12
Since
= X +2 whenever x# 6, it follows that the two expressions evaluate to the same number as x approaches 6.
X-6
ов.
X-4x- 12
The limits lim
and lim (x+ 2) equal the same number when evaluated using direct substitution.
X- 6
X6
C. Since each limit approaches 6, it follows that the limits are equal.
2
X - 4x- 12
D.
The numerator of the expression
simplifies to x +2 for all x, so the limits are equal.
X - 6
Now evaluate the limit.
X- 4x - 12
lim
(Simplify your answer.)
X- 6
X→6

Expert Solution

Step 1

$Given that : \lim_{x \to 6} \frac{x^{2} - 4 x - 12}{x - 6} = \lim_{x \to 6} (x + 2) To evaluate \lim_{x \to 6} \frac{x^{2} - 4 x - 12}{x - 6}$

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