Chapter 1: Q. 27 (page 135)

Calculate the limits using only the continuity of linear and power functions and the limit rules. Cite each limit rule that you apply.
$\lim_{x \to 3} (3 x + x^{2} (2 x + 1))$

Short Answer

Expert verified

On calculating the limits, we get,

$72$

Step by step solution

Step 1. Given information.

Consider the given question,

$\lim_{x \to 3} (3 x + x^{2} (2 x + 1))$

Step 2. Calculate the limits.

Using the sum rule,

$= \lim_{x \to 3} (3 x) + \lim_{x \to 3} (x^{2} (2 x + 1))$

Using the product rule,

$= \lim_{x \to 3} (3 x) + \lim_{x \to 3} (x^{2}) \lim_{x \to 3} (2 x + 1) = 3 (3) + 3^{2} (2 \cdot 3 + 1) = 9 + 9 (6 + 1) = 9 + 9 (7) = 72$

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Calculate the limits using only the continuity of linear and power functions and the limit rules. Cite each limit rule that you apply.
$\lim_{x \to 3} (3 x + x^{2} (2 x + 1))$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculate the limits.

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Calculate the limits using only the continuity of linear and power functions and the limit rules. Cite each limit rule that you apply.limx→33x+x22x+1

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculate the limits.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

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Study anywhere. Anytime. Across all devices.

Calculate the limits using only the continuity of linear and power functions and the limit rules. Cite each limit rule that you apply.
$\lim_{x \to 3} (3 x + x^{2} (2 x + 1))$