Chapter 14: Q. 12 (page 876)

In Problems 7–16, use a table to find the indicated limit.
$12 . \lim_{x \to 3} = \frac{x^{2} - 9}{x^{2} - 3 x}$ .

Short Answer

Expert verified

$\lim_{x \to 3} \frac{x^{2} - 9}{x^{2} - 3 x} = 2$ .

Step by step solution

Step 1. Given information.

Given function is $f (x) = \frac{x^{2} - 9}{x^{2} - 3 x}$ whose limit tend to 3 need to be found.

Step 2. The table is as follows.

Compare the given limit to.
Choose values of x close to 3, arbitrarily starting with 2.99 then we select additional numbers that get closer to 3, but remain less than 3. Next choose values of x greater than 3, staring with 3.01, which get closer to3.

Finally evaluate f(x) at each choice to obtain the required Table.

As x gets closer to 3 then f(x) gets closer to 2.

So, $\lim_{x \to 3} \frac{x^{2} - 9}{x^{2} - 3 x} = 2$ .

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In Problems 7–16, use a table to find the indicated limit.
$12 . \lim_{x \to 3} = \frac{x^{2} - 9}{x^{2} - 3 x}$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. The table is as follows.

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In Problems 7–16, use a table to find the indicated limit.12.limx→3=x2-9x2-3x.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. The table is as follows.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Mechanics Maths

Theoretical and Mathematical Physics

Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In Problems 7–16, use a table to find the indicated limit.
$12 . \lim_{x \to 3} = \frac{x^{2} - 9}{x^{2} - 3 x}$ .