Ma 113 Functions And Inverse Functions, The Exponential Function And The Logarithm Worksheet Page 11
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41x
3
11. If f (x) =
, find lim
f (x), lim
f (x) and lim
f (x).
2
x
x
6
x
3
x
3
x
3
12. (a) State the definition of the continuity of a function f (x) at x = a.
(b) Find the constant a so that the function is continuous on the entire real line.
2
2
x
a
if x = a
f (x) =
x
a
8
if x = a
13. Complete the following statements:
(a) A function f (x) passes the horizontal line test, if the function f is ................
(b) If lim
f (x) and lim
g(x) exist, then
x
a
x
a
lim
f (x)
f (x)
x
a
lim
=
provided ..................
g(x)
lim
g(x)
x
a
x
a
(c) lim
f (x) = lim
f (x) = L if and only if ...................
x
a
x
a
x if x = 2
(d) Let g(x) =
be a piecewise function.
1
if x = 2
The function g(x) is NOT continuous at x = 2 since .................................
2
x
if x < 0
(e) Let f (x) =
1
if x = 0
be a piecewise function.
x
if x > 0
The function f (x) is NOT continuous at x = 0 since .................................
2
x
14. If g(x) = x
+ 5
3, use the Intermediate Value Theorem to show that there is a number a such that
g(a) = 10.
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