Different quotient (and similar) practice problems
Different quotient (and similar) practice problems
1. For each of the following functions, simplify the expression
f (x + h) - f (x) h
as far as possible. In particular, you should be able to rewrite each expression without an h in the denominator.
(a) f (x) = 2x + 5
(b) f (x) = 3 - x (c) f (x) = x2
(d) f (x) = 2x2 - x
(e)
f (x) =
1 2
x2
+
3x
-
4
(f) f (x) = x
(g) f (x) = x2 - 1
2. For each of the following functions, simplify the expression
f (x + h) - f (x + 2h) h
as far as possible. In particular, you should be able to rewrite each expression without an h in the denominator.
(a) f (x) = 5
(b) f (x) = x + 3
(c)
f (x) =
2 3
x2
-
1
(d) f (x) = x2 + 4x - 6
Answers:
1. (a) 2
(b) -1
(c) 2x + h
(d) 4x + 2h - 1
(e)
x+
1 2
h
+
3
1 (f) x + h + x
2x + h (g) (x + h)2 - 1 + x2 - 1
2. (a) 0
(b) -1
(c)
-
4 3
x
-
2h
(d) -2x - 3h - 4
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