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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.
$\lim_{x 鈫� 3} (3 x + x^{2} (2 x + 1))$

Short Answer

Expert verified

On calculating the limits, we get,

$72$

Step by step solution

01

Step 1. Given information.

Consider the given question,

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

02

Step 2. Calculate the limits.

Using the sum rule,

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

Using the product rule,

$= \lim_{x 鈫� 3} (3 x) + \lim_{x 鈫� 3} (x^{2}) \lim_{x 鈫� 3} (2 x + 1) = 3 (3) + 3^{2} (2 路 3 + 1) = 9 + 9 (6 + 1) = 9 + 9 (7) = 72$

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$\lim_{x 鈫� 蟺} \frac{1}{\cos e c (蟺 - x)}$

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