Unformatted text preview: = x2 − x − 2 with the
quantity (x + h) to get
f (x + h) = (x + h)2 − (x + h) − 2
= x2 + 2xh + h2 − x − h − 2.
So the diﬀerence quotient is
f (x + h) − f (x)
h
2 = x2 + 2xh + h2 − x − h − 2 − x2 − x − 2
h You may need to brush up on your Intermediate Algebra skills, as well. 1.6 Function Arithmetic 59
x2 + 2xh + h2 − x − h − 2 − x2 + x + 2
h
2−h
2xh + h
h
h (2x + h − 1)
h
h
(2x + h − 1)
h
=
=
=
=
= factor
cancel 2x + h − 1. 2. To ﬁnd g (x + h), we replace every occurrence of x in the formula g (x) =
quantity (x + h) g (x + h) = 3
2(x + h) + 1 = 3
with the
2x + 1 3
,
2x + 2 h + 1 which yields
g (x + h) − g (x)
h =
= 3
3
−
2x + 2 h + 1 2x + 1
h
3
3
−
2x + 2h + 1 2x + 1 · (2x + 2h + 1)(2x + 1)
h
(2x + 2h + 1)(2x + 1) = 3(2x + 1) − 3(2x + 2h + 1)
h(2x + 2h + 1)(2x + 1) = 6x + 3 − 6x − 6h − 3
h(2x + 2h + 1)(2x + 1) = −6h
h(2x + 2h + 1)(2x + 1) = −6
h
h
(2x + 2h + 1)(2x + 1) = −6
.
(2x + 2h + 1)(2x + 1) For reasons which will become clear in Cal...
View
Full Document
 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

Click to edit the document details