Chapter 14: Q. 15 (page 876)

In Problems 7–16, use a table to find the indicated limit.
$15 . \lim_{x \to 0} \frac{\cos x - 1}{x}, x$ in radians.

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

Given a function is $f (x) = \frac{\cos x - 1}{x}$ whose limit needs to be found tending to 0.

Step 2. The table is as follows.

Compare the given limit 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 evaluatef(x) at each choice to obtain the required Table.

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

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

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In Problems 7–16, use a table to find the indicated limit.
$15 . \lim_{x \to 0} \frac{\cos x - 1}{x}, x$ in radians.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. The table is as follows.

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In Problems 7–16, use a table to find the indicated limit.15.limx→0cosx-1x,xin radians.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. The table is as follows.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

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Study anywhere. Anytime. Across all devices.

In Problems 7–16, use a table to find the indicated limit.
$15 . \lim_{x \to 0} \frac{\cos x - 1}{x}, x$ in radians.