# Solve Limit Problems on a Calculator Using the Arrow-Number

A limit problem asks you to determine what the y value of a function is zeroing in on as the x value approaches a particular number. You can solve a limit problem with your calculator using the arrow-number.

First, store a number into x that’s extremely close to the arrow-number, enter the limit expression in the home screen, and hit *enter*. If you get a result really close to a round number, that’s your answer—you’re done. If you have any doubt about the answer, just store another number into x that’s even closer to the arrow-number, get back to the limit expression, and hit enter again. This will likely give you a result even closer to the same round number—that’s it; you’ve got it.

This method can be the quickest, but it often doesn’t give you a good feel for how the y values zero in on the result. To get a better picture of this process, you can store three or four numbers into x (one after another), each a bit closer to the arrow-number, and look at the sequence of results.

## Practice questions

- Evaluate

- Use your calculator to evaluate

## Answers and explanations

**The answer is 7.**

**Step 1.**Use the*STO*button to store 6.01 into*x*.

**Step 2.**Enter

on the home screen and hit*enter*. (Note: You must be in*radian*mode.)

This gives you a result of ~7.01, suggesting that the answer is 7.

**Step 3.**Repeat Steps 1 and 2 with 6.001 stored into*x*.

This gives you a result of ~7.001.

**Step 4.**Repeat Steps 1 and 2 with 6.0001 stored into*x*.

This gives you a result of ~7.0001.

Because the results are obviously homing in on the round number of 7, that’s your answer.**The answer is –11.**You want the limit as

*x*approaches –3, so pick a number really close to –3, like –3.0001, plug that into*x*in your function

and enter that into your calculator. For example, if you’ve got a calculator like a Texas Instruments TI-84, a good way to do this is to use the*STO*button to store –3.0001 into*x*, then enter

into the home screen and punch

*enter*.

The calculator’s answer is –11.0001. Because this is near the round number –11, your answer is –11. By the way, you can do this problem easily with algebra as well.