Chapter 1: Q. 43 (page 88)

Use tables of values to make educated guesses for each of the limits in Exercises 39–52.
$\lim_{x \to 3} \frac{x - 3}{(x^{2} - 2) (x - 3)}$

Short Answer

Expert verified

The value is $0.413 .$

Step by step solution

Step 1. Given information.

The given function is $\lim_{x \to 3} \frac{x - 3}{(x^{2} - 2) (x - 3)} .$

Step 2. Table of values.

Consider the table,

$x$	$2.9$	$2.99$	$2.999$	$3$	$3.001$	$3.01$	$3.1$
$\frac{x - 3}{(x^{2} - 2) (x - 3)}$	$0.156$	$0.144$	$0.143$	*	$0.143$	$0.143$	$0.131$

The value of $\frac{x - 3}{(x^{2} - 2) (x - 3)}$ approaches to $0.143$ to the left and right.

Therefore, $\lim_{x \to 3} \frac{x - 3}{(x^{2} - 2) (x - 3)} = 0.143$

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Use tables of values to make educated guesses for each of the limits in Exercises 39–52.
$\lim_{x \to 3} \frac{x - 3}{(x^{2} - 2) (x - 3)}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Table of values.

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Use tables of values to make educated guesses for each of the limits in Exercises 39–52.limx→3x-3x2-2(x-3)

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Table of values.

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Use tables of values to make educated guesses for each of the limits in Exercises 39–52.
$\lim_{x \to 3} \frac{x - 3}{(x^{2} - 2) (x - 3)}$