Evaluating limits – Sharp EL-9900 User Manual
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Advanced Keyboard/CALCULUS USING THE SHARP EL-9900
Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only.
1.
Set the calculator to floating point decimal display by pressing 2ndF
SET UP C (FSE) and 1 (Float Pt). Set the calculator to rectangular
coordinates E (COORD) and 1 (Rect). Press 2ndF QUIT to exit the
set up menu.
2.
Consider the function f(x) = . Press Y= CL to access and clear the
Y1 prompt. Press ENTER CL to clear the remaining prompts.
3.
Construct a graph of f(x) in the Decimal viewing window by first entering
Y1= with the keystrokes a/b 2 X/
θ/T/n + 2 X/θ/T/n
x
2
– 1 , and then press ZOOM A (ZOOM) 7 (Dec) to see
the graph.
4.
Notice that even though is not defined at x = -1 (as evidenced by the
hole in the graph at that point), the functional values appear to be getting
closer and closer to -1. A careful observation of the graph leads to the
following estimates:
lim f(x) = 0,
x
→ -∞
lim f(x) = -1,
x
→ -1
lim f(x) does not exist,
x
→ 1
and lim f(x) = 0.
x
→ ∞
5.
It also appears that the line y = 0 is a horizontal asymptote and the line x = 1
is a vertical asymptote for this function.
EVALUATING LIMITS
(2x + 2)
(x
2
– 1)
(2x + 2)
(x
2
– 1)
(2x + 2)
(x
2
– 1)
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