Chapter 10: Q. 28 (page 777)

Calculate the limits in Exercises $25 - 28$ , using only the continuity of linear and power functions and the limit rules. Cite each limit rule that you apply.
localid="1648227587052" $\lim_{x \to 0} \frac{3}{2 x^{2} - 4 x + 1}$ .

Short Answer

Expert verified

The value of $\lim_{x \to 0} \frac{3}{2 x^{2} - 4 x + 1}$ is, $3 .$

Step by step solution

Step 1. Given information

$\lim_{x \to 0} \frac{3}{2 x^{2} - 4 x + 1}$ .

Step 2. The limit is calculated as below,

$\lim_{x \to 0} \frac{3}{2 x^{2} - 4 x + 1} = \frac{\lim_{x \to 0} 3}{\lim_{x \to 0} (2 x^{2} - 4 x + 1)}$ [Quotient rule]

$= \frac{\lim_{x \to 0} 3}{\lim_{x \to 0} (2 x^{2}) - \lim_{x \to 0} 4 x + \lim_{x \to 0} (1)}$ [Sum rule]

$= \frac{3}{(2 \cdot 0) - (4 \cdot 0) + 1} = \frac{3}{1} = 3$

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Calculate the limits in Exercises $25 - 28$ , using only the continuity of linear and power functions and the limit rules. Cite each limit rule that you apply.
localid="1648227587052" $\lim_{x \to 0} \frac{3}{2 x^{2} - 4 x + 1}$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. The limit is calculated as below,

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Calculate the limits in Exercises 25-28, using only the continuity of linear and power functions and the limit rules. Cite each limit rule that you apply.localid="1648227587052" limx→032x2-4x+1.

Short Answer

Step by step solution

Step 1. Given information

Step 2. The limit is calculated as below,

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Mechanics Maths

Discrete Mathematics

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Geometry

Study anywhere. Anytime. Across all devices.

Calculate the limits in Exercises $25 - 28$ , using only the continuity of linear and power functions and the limit rules. Cite each limit rule that you apply.
localid="1648227587052" $\lim_{x \to 0} \frac{3}{2 x^{2} - 4 x + 1}$ .