Tutorial Exercise Use the given graph of the function y = f(x) to find the following quantities, if they exist. y 6- 4 3 1 -6 -5 -4 -3 -2 -1 1 2 (a) lim f(x) x--4 (b) lim f(x) x--1 (c) lim f(x) x--1+ (d) lim f(x) x--1 (e) f(-1) Step 1 of 3 2.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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. Similarly, lim f(x) = L if the values of f(x) can be made arbitrarily close to L by taking x sufficiently close to a
x→a+
for 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
Transcribed Image Text: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. Similarly, lim f(x) = L if the values of f(x) can be made arbitrarily close to L by taking x sufficiently close to a x→a+ for 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
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