Question

In Problems 7–16, use a table to find the indicated limit.

$15.\underset{x\to 0}{\lim }\frac{\cos x-1}{x},x$in radians.

Short answer

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

Step-by-step solution

Step 1. Given information.

Given a function is $f\left(x\right)=\frac{\cos x-1}{x}$ 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,$\underset{x\to 0}{\lim }\frac{\cos x-1}{x}=0$, x in radians.