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How to estimate a limit with a table on a TI-84 Plus CE, TI-84 Plus or TI-83 Plus

By E-Code · updated

Press 2nd TBLSET (above WINDOW), set Indpnt to Ask, then open 2nd TABLE and type X values closer and closer to the point, pressing ▼ before each new one. The Y1 column heads to the limit: sin(X)/X goes to 1 as X nears 0.

Before you start

Type the function into the Y= editor first: this guide uses Y1 = sin(X)/X (Y=, SIN, X,T,θ,n, ), ÷, X,T,θ,n, then 2nd QUIT).

Y= SIN X,T,θ,n ) ÷ X,T,θ,n 2nd MODE

Step by step

  1. Open TBLSET. 2nd WINDOW Press 2nd, then WINDOW. Y1 = sin(X)/X is already typed in for you.
  2. Go down to Indpnt. ▼ ▼ Press ▼ twice to the Indpnt row: it decides who picks the X values.
  3. Move to Ask. ▶ Press ▶ onto Ask.
  4. Pick Ask. ENTER Press ENTER. Now the table waits for you to type each X.
  5. Open the table. 2nd GRAPH Press 2nd, then GRAPH (TABLE). It starts empty.
  6. Try X = 0.1. . 1 ENTER Type .1 and ENTER. Y1 is worked out next to it.
  7. Closer: X = 0.01. ▼ . 0 1 ENTER Press ▼ to the next row, then type .01 and ENTER.
  8. Closer still: X = 0.001. ▼ . 0 0 1 ENTER Press ▼, then type .001 and ENTER.
  9. Read Y1 in full. ▶ Press ▶ onto the Y1 value. The line at the bottom shows it with every digit.
  10. Heading to 1. Y1 goes .9983, .99998, .9999998 as X nears 0: the limit of sin(X)/X at 0 is 1, even though X = 0 itself gives an error.

What the screen shows

Y1 goes .9983, .99998, .9999998 as X nears 0: the limit of sin(X)/X at 0 is 1, even though X = 0 itself gives an error.

Look for Y1=.9999998333 on the screen.

Try it with the keys lit up

This guide is one of E-Code's Learn lessons. Open it on E-Code's TI-84 calculator and each key lights up in turn as you press it.

Try “Estimate a limit with a table” on the TI-84 calculator

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