Chapter 14: Q. 16 (page 876)

In Problems 7–16, use a table to find the indicated limit.
$16 . \lim_{x \to 0} \frac{\tan x}{x}, x$ in radians.

Short Answer

Expert verified

$\lim_{x \to 0} \frac{\tan x}{x} = 1, x$ in radians.

Step by step solution

Step 1. Given.

A function is $f (x) = \frac{\tan x}{x}$ whose limit needs to be found tending to 0.

Step 2. The table is as follows.

Compare the given function to .

Choose values of x close to 0 , arbitrarily starting with -0.01. Then we select additional numbers that get closer to 0 , but remain less than 0 .

Next choose values of x greater than 0 , staring with 0.01, which get closer to 0 .

Finally evaluate f(x) at each choice to obtain the required Table.

As x gets closer to 0 then f(x) gets closer to 1.

So, $\lim_{x \to 0} \frac{\tan x}{x} = 1, x$ in radians.

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In Problems 7–16, use a table to find the indicated limit.
$16 . \lim_{x \to 0} \frac{\tan x}{x}, x$ in radians.

Short Answer

Step by step solution

Step 1. Given.

Step 2. The table is as follows.

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In Problems 7–16, use a table to find the indicated limit.16.limx→0tanxx,xin radians.

Short Answer

Step by step solution

Step 1. Given.

Step 2. The table is as follows.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In Problems 7–16, use a table to find the indicated limit.
$16 . \lim_{x \to 0} \frac{\tan x}{x}, x$ in radians.