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Chapter 1: Q. 12 (page 153)

Consider the limit expression
$\lim_{x \to \frac{π}{2}} \frac{\sin x}{x}$
Calculate the limit.

Short Answer

Expert verified

The limit of the expression is $\frac{2}{π}$ .

Step by step solution

Step 1. Given

The given expression is

$\lim_{x \to \frac{π}{2}} \frac{\sin x}{x}$ .

Step 2. Calculation

The evaluation of the equation is

$\lim_{x \to \frac{π}{2}} {\frac{\sin x}{x}}_{} = {\frac{\sin \frac{π}{2}}{\frac{π}{2}}}_{} = \frac{1}{\frac{π}{2}} = \frac{2}{π}$

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Most popular questions from this chapter

Write each of the inequalities in interval notation:

$0 < | x - 2 | < 0.1$

For each function f graphed in Exercises 23–26, describe the intervals on which f is continuous. For each discontinuity of f, describe the type of discontinuity and any one-sided continuity. Justify your answers about discontinuities with limit statements.

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Write each of the inequalities in interval notation:

$|f (x) - L| < \in$

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Consider the limit expressionlimx→π2sinxxCalculate the limit.

Short Answer

Step by step solution

Step 1. Given

Step 2. Calculation

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Consider the limit expression
$\lim_{x \to \frac{π}{2}} \frac{\sin x}{x}$
Calculate the limit.