Let f(x) = (x + 2)/(x^{2} - 3x + 2). a) Find \lim_{x \rightarrow \infty} f(x) b) Find ...

Question:

Let

$$f(x) = \frac{x + 2}{x^{2} - 3x + 2} $$

a) Find

$$\lim_{x \rightarrow \infty} f(x) $$

b) Find

$$\lim_{x \rightarrow 1} f(x) $$

c) Find the vertical and horizontal asymptotes of {eq}f(x) {/eq}.

d) Find the x-value at which {eq}f(x) {/eq} is not continuous.

e) If there is any removable discontinuity for {eq}f(x) {/eq}, then remove it by defining a new function of {eq}\hat{f}(x) {/eq}.

Continuous functions

A function is continuous if the function has not asymptotes nor holes, a function is continuous if the function is differentiable for all values its domain.

Answer and Explanation:

{eq}a). \displaystyle \lim_{x \rightarrow \infty} f(x)= \lim_{x \rightarrow \infty} \frac{x + 2}{x^{2} - 3x + 2}= 0 \\ b). \displaystyle \lim_{x...

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Continuous Functions Theorems

from GRE Math: Study Guide & Test Prep

Chapter 5 / Lesson 10
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