156
Chapter 2 | Limits
calculator to graph the function and determine the limit. Was the conjecture correct? If not, why does the method of tables fail?
⎛ ⎝ π θ
⎞ ⎠
44. lim θ →0
sin
⎛ ⎝
⎞ ⎠
⎛ ⎝
⎞ ⎠
π θ
π θ
sin
sin
θ
θ
−0.1
a.
0.1
e.
−0.01
b.
0.01
f.
−0.001
c.
0.001
g.
−0.0001 d.
0.0001 h.
⎛ ⎝ π α
⎞ ⎠
1 α cos
lim α →0 +
45.
1 α cos
π α
⎛ ⎝
⎞ ⎠
a
f ( x ) =0
lim x →10
46.
0.1
a.
f ( x ) =3
lim x →−2 +
47.
0.01
b.
f ( x ) = f (−8)
lim x →−8
48.
f ( x ) =5
49. lim x →6
0.001
c.
In the following exercises, use the following graph of the function y = f ( x ) to find the values, if possible. Estimate when necessary.
0.0001 d.
In the following exercises, consider the graph of the function y = f ( x ) shown here. Which of the statements about y = f ( x ) are true and which are false? Explain why a statement is false.
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