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 = x 2 e − 2 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 = x 2 e − 2 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.
Determine value for c so that lim f(x) x--> 3 exists
f(x)= 1/3x+c For x<3
-x+8 For x>3
Sketch the graph of a function f that satisfies all of the given conditions.
lim f(x) = 4, lim
x+3+
x→3
f(x) :
= 2, lim, f(x) = 2, f(3) = 3, f(–2) = 1
x→-2
البارب
برای
-6
-6
-4
-4
-2
-2
5
4
3
y
4
2
1
-1
2
2
4
4
6
x
-6
-4
-2
5
4
3
1
2
4
6
X
-6
-4
●
-2
I
y
5
4
3
1
....لي
2
4
6
x
Sketch an example of a function that satisfies the following conditions:
lim f(x) = ∞
x→2-
• lim f(x) = -∞
x→2+
• There is a jump discontinuity at x = -1.
• f'(-3) = 0
lim f(x)
= -
X-00
• lim f(x) = -4
x00
Chapter 4 Solutions
Calculus Early Transcendentals, Binder Ready Version
Thomas' Calculus: Early Transcendentals (14th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY