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Chapter 14: Q. 16 (page 876)

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

16.limx鈫�0tanxx,xin radians.

Short Answer

Expert verified

limx鈫�0tanxx=1,x in radians.

Step by step solution

01

Step 1. Given.

A function is f(x)=tanxx whose limit needs to be found tending to 0.

02

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,limx鈫�0tanxx=1,xin radians.

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