# How do you find limits on a graphing calculator?

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Wataru Share
Sep 24, 2014

I am not sure if there is a TI-84 Plus function that directly finds the value of a limit; however, there is a way to approximate it by using a table. Let us approximate the value of the limit

${\lim}_{x \to 1} \frac{\sqrt{x + 3} - 2}{x - 1}$

Step 1: Go to "Y=", then type in the function.

Step 2: Go to "TBL SET" (2nd+WINDOW), then set TblStart=.97 and $\Delta$Tbl=.01.

(Note: TblStart is the starting x-value in the table, so put a number slightly smaller that the number x approaches. $\Delta$Tbl is the increment value in the x-column, so make it sufficiently small for the precision you need.)

Step 3: Go to "" TABLE (2nd+GRAPH).

As you can see in the table above, the function value (${Y}_{1}$) approaches 0.25 (or 1/4) as x approaches 1; therefore, we conclude that

${\lim}_{x \to 1} \frac{\sqrt{x + 3} - 2}{x - 1} = \frac{1}{4}$

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