Using L'H o ^ pital's rule (Section 3.6) one can verify that lim x → + ∞ e x x = + ∞ , lim x → + ∞ x e x = 0 , lim x → − ∞ x e x = 0 In these exercises: (a) Use these results, as necessary, to find the limits of f x as x → + ∞ and as x → − ∞ . (b) Sketch a graph of f x and identify all relative extrema, inflection points, and asymptotes (as appropriate). Check your work with a graphing utility. f x = e x 1 − x
Using L'H o ^ pital's rule (Section 3.6) one can verify that lim x → + ∞ e x x = + ∞ , lim x → + ∞ x e x = 0 , lim x → − ∞ x e x = 0 In these exercises: (a) Use these results, as necessary, to find the limits of f x as x → + ∞ and as x → − ∞ . (b) Sketch a graph of f x and identify all relative extrema, inflection points, and asymptotes (as appropriate). Check your work with a graphing utility. f x = e x 1 − x
Using
L'H
o
^
pital's
rule (Section 3.6) one can verify that
lim
x
→
+
∞
e
x
x
=
+
∞
,
lim
x
→
+
∞
x
e
x
=
0
,
lim
x
→
−
∞
x
e
x
=
0
In these exercises: (a) Use these results, as necessary, to find the limits of
f
x
as
x
→
+
∞
and as
x
→
−
∞
. (b) Sketch a graph of
f
x
and identify all relative extrema, inflection points, and asymptotes (as appropriate). Check your work with a graphing utility.
3. In the space below, describe in what ways the
function f(x) = -2√x - 3 has been
transformed from the basic function √x. The
graph f(x) on the coordinate plane at right.
(4 points)
-4
-&-
-3
--
-2
4
3-
2
1-
1 0
1
2
-N
-1-
-2-
-3-
-4-
3
++
4
2. Suppose the graph below left is the function f(x). In the space below, describe what
transformations are occuring in the transformed function 3ƒ(-2x) + 1. The graph it on the
coordinate plane below right. (4 points)
1
1. Suppose we have the function f(x) = = and then we transform it by moving it four units to the
right and six units down, reflecting it horizontally, and stretching vertically by 5 units. What will
the formula of our new function g(x) be? (2 points)
g(x) =
Chapter 4 Solutions
Calculus Early Transcendentals, Binder Ready Version
Elementary Statistics: Picturing the World (7th Edition)
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