Calculus
10th Edition
ISBN: 9781285948133
Author: Ron Larson; Bruce H. Edwards
Publisher: Cengage Learning US
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Textbook Question
Chapter 1, Problem 5RE
Finding a Limit Graphically In Exercises 5 and 6, use the graph to find the limit (if it exists). If the limit does not exist, explain why.
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Tutorial Exercise
Use the given graph of the function y = f(x) to find the following quantities, if they exist.
y
3
1
-6
-5
-4
-3
-2
-1
1
(a)
lim f(x)
X-4
(b)
lim
f(x)
X-1-
(c)
x--1+
lim
f(x)
(d)
lim f(x)
x--1
(e) f(-1)
Step 1 of 3
(a)
lim f(x)
X→-4
Recall lim f(x) exists if and only if lim f(x) =
lim f(x).
a+
Xa
Xa
Also recall lim f(x) = L if the values of f(x) can be made arbitrarily close to L by taking x sufficiently close to a for
Xa
x a.
Using the graph, find the values (if they exist) of
lim f(x) and
lim f(x). (If a limit does not exist, enter DNE.)
X→-4+
X-4-
lim
f(x) =
X→-4-
lim
f(x) =
X→-4+
O, lim f(x) ---Select---
X--4
O and its value is as follows. (If the limit does not
Since these limits
-Select---
exist, enter DNE.)
lim f(x) =
X-4
Find each limit, state it does not exist.
1
(a) lim f(x)
(b) lim f(x)
(c) lim f(x)
x→2+
x→-3+
x→-3
(d) lim f(x)
(b) lim f(x)
(c) lim f(x)
x+4
x→2-
2.
Determine the infinite limit (show the details).
X-2
(a) lim
x-4-X-4
X-3
(b) lim
→2 (x- 2)2
(Hint: You don't need to evaluate the limits, you just need to determine whether the limits are
-00 or 0)
Chapter 1 Solutions
Calculus
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Prove that if...
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- I've never seen a limit question like this. How do I decide limits with so many small lines?arrow_forwardQuestion: What does the graph of f(x) say about the value of lim f(x)? x->-1+ y -3 -2 2 3arrow_forwardSkz - 3, IS-1 S(x) = - 2+ k, 1>-1 find the value k such that lim f(x) exists. Given x-1arrow_forward
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Limits and Continuity; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=9brk313DjV8;License: Standard YouTube License, CC-BY