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Chapter 1: Q. 70 (page 149)

Calculate each limit in Exercises 35鈥�80.
$\underset{x 鈫� 0}{l i m} \frac{3 \sin x + x}{x}$

Short Answer

Expert verified

The limit is 4

Step by step solution

01

Step 1. Given information

The given expression is $\underset{x 鈫� 0}{l i m} \frac{3 \sin x + x}{x}$

02

Step 2. Calculation

The limit is calculated as below,

$[From definition, \underset{胃鈫� 0}{l i m} \frac{\sin 胃}{胃} = 1] \underset{x 鈫� 0}{l i m} \frac{3 \sin x + x}{x} = \underset{x 鈫� 0}{l i m} (\frac{3 \sin x}{x} + \frac{x}{x}) = \underset{x 鈫� 0}{l i m} (\frac{3 \sin x}{x} + 1) = 3 \underset{x 鈫� 0}{l i m} (\frac{\sin x}{x}) + \underset{x 鈫� 0}{l i m} 1 = 3 (1) + 1 = 4$

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Most popular questions from this chapter

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