Chapter 1: Q. 7 (page 119)

Given the following function $f$ , define $f (1)$ so that $f$ is continuous at x = 1, if possible:
$f (x) = \frac{x^{2} - 2 x + 1}{x^{2} - 6 x + 5}$

Short Answer

Expert verified

After taking limit

$\lim_{x \to 1} \frac{x^{2} - 2 x + 1}{x^{2} - 6 x + 5} = 0$

Step by step solution

Step 1. Given information

Function $f (x) = \frac{x^{2} - 2 x + 1}{x^{2} - 6 x + 5}$

Step 2. Taking limit in the function

$\lim_{x \to 1} f (x) = \lim_{x \to 1} \frac{x^{2} - 2 x + 1}{x^{2} - 6 x + 5} = \lim_{x \to 1} \frac{{(x - 1)}^{2}}{x^{2} - 5 x - x + 5} = \lim_{x \to 1} \frac{{(x - 1)}^{2}}{x (x - 5) - 1 (x - 5)} = \lim_{x \to 1} \frac{{(x - 1)}^{2}}{(x - 5) (x - 1)} = \lim_{x \to 1} \frac{(x - 1)}{(x - 5)} = \frac{\lim_{x \to 1} (x - 1)}{\lim_{x \to 1} (x - 5)} = \frac{1 - 1}{1 - 5} = \frac{0}{- 4} = 0$

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Given the following function $f$ , define $f (1)$ so that $f$ is continuous at x = 1, if possible:
$f (x) = \frac{x^{2} - 2 x + 1}{x^{2} - 6 x + 5}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Taking limit in the function

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Given the following function f, define f(1)so that fis continuous at x = 1, if possible:f(x)=x2-2x+1x2-6x+5

Short Answer

Step by step solution

Step 1. Given information

Step 2. Taking limit in the function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

Probability and Statistics

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Geometry

Study anywhere. Anytime. Across all devices.

Given the following function $f$ , define $f (1)$ so that $f$ is continuous at x = 1, if possible:
$f (x) = \frac{x^{2} - 2 x + 1}{x^{2} - 6 x + 5}$