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3x? - 4x Limit of a rational function Evaluate lim xS2 5x - 36

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.6: Rational Functions

Problem 91E

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Question

3x? - 4x
Limit of a rational function Evaluate lim
xS2 5x - 36

Expert Solution

Step 1

We have to find the limit:

$\lim_{x \to 2} \frac{3 x^{2} - 4 x}{5 x^{3} - 36}$

Since this is determinate limit so we just have to put the value of limit into the function.

So putting $x = 2$ into the function,

$\begin{array}{rcl} \lim_{x \to 2} \frac{3 x^{2} - 4 x}{5 x^{3} - 36} & = & \frac{3 {(2)}^{2} - 4 (2)}{5 {(2)}^{3} - 36} \\ = & \frac{3 \times 4 - 8}{5 \times 8 - 36} \end{array}$

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