Question

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

$16.\underset{x\to 0}{\lim }\frac{\tan x}{x},x$in radians.

Short answer

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

Step-by-step solution

Step 1. Given.

A function is $f\left(x\right)=\frac{\tan x}{x}$ 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,$\underset{x\to 0}{\lim }\frac{\tan x}{x}=1,x$in radians.