Page 61 - Calculus Workbook For Dummies

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Chapter 4: Nitty-Gritty Limit Problems

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Q. Evaluate lim x - 5 x - 6 . 3. Go to the Table and you’ll see the
^
x " 6 sin x - 6h y-values getting closer and closer to
A. The answer is 7. 7 as you scroll toward x = 6 from
above and below 6.
Method I.
So 7 is your answer.
1. Use the STO → button to store 6.01 Method III.
into x. x - 5 x - 6
2
2
x - 5 x - 6 1. Enter in graphing
2. Enter on the home sin x - 6h
^
sin x - 6h mode again.
^
screen and hit enter. (Note: You
must be in radian mode.) 2. Graph the function. For your first
viewing, ZoomStd, ZoomFit, and
This gives you a result of ~7.01, sug- ZoomTrig (for expressions contain-
gesting that the answer is 7.
ing trig functions) are good win-
3. Repeat Steps 1 and 2 with 6.001 dows to try.
stored into x.
For this funny function, none of
This gives you a result of ~7.001. these three window options works
very well, but ZoomStd is the best.
4. Repeat Steps 1 and 2 with 6.0001
stored into x. 3. Trace close to x = 6 and you’ll see
that y is near 7. Use ZoomBox to
This gives you a result of ~7.0001. draw a little box around the point
Because the results are obviously _ , 6 7i then hit enter.
honing in on the round number of 7,
that’s your answer. 4. Trace near x = 6 on this zoomed-in
graph until you get very near to
Method II.
x = 6.
2
x - 5 x - 6
1. Enter in graphing or
sin x - 6h 5. Repeat the Zoombox process
^
“y =” mode. maybe two more times and you
should be able to trace extremely
2. Go to Table Setup and set tblStart close to x = 6.
to the arrow-number, 6, and ∆Tbl
to 0.01. (When I did this, I could trace to
x = 6.0000022, y = 7.0000023.)
The answer is 7.
13. Use your calculator to evaluate 14. Use your calculator to determine
2
x - 5 x - 24 sinx
lim . Try all three methods. lim 1 . Use all three methods.
-
x " - 3 x + 3 x " 0 tan x
Solve It Solve It