Explain what it means to say that lim f(x) = 7 x-3" lim f(x) = 9. and x+ 3* As x approaches 3, f(x) approaches 7, but f(3) = 9. %3! As x approaches 3 from the left, f(x) approaches 7. As x approaches 3 from the right, f(x) approaches 9. O As x approaches 3, f(x) approaches 9, but f(3) = 7. O As x approaches 3 from the right, f(x) approaches 7. As x approaches 3 from the left, f(x) approaches 9. In this situation is it possible that lim f(x) exists? Explain. O Yes, f(x) could have a hole at (3, 7) and be defined such that f(3) = 9. O Yes, f(x) could have a hole at (3, 9) and be defined such that f(3) = 7. O Yes, if f(x) has a vertical asymptote at x = 3, it can be defined such that lim f(x) = 7, lim f(x) = 9, and lim f(x) exists. X3" x-3+ x--3 No, lim f(x) cannot exist if lim f(x) * lim f(x). X3 X-3+

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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Explain what it means to say that
lim f(x) = 7
x-3"
lim f(x) = 9.
and
x+ 3*
As x approaches 3, f(x) approaches 7, but f(3) = 9.
%3!
As x approaches 3 from the left, f(x) approaches 7. As x approaches 3 from the right, f(x) approaches 9.
O As x approaches 3, f(x) approaches 9, but f(3) = 7.
O As x approaches 3 from the right, f(x) approaches 7. As x approaches 3 from the left, f(x) approaches 9.
In this situation is it possible that lim f(x) exists? Explain.
O Yes, f(x) could have a hole at (3, 7) and be defined such that f(3) = 9.
O Yes, f(x) could have a hole at (3, 9) and be defined such that f(3) = 7.
O Yes, if f(x) has a vertical asymptote at x = 3, it can be defined such that lim f(x) = 7, lim f(x) = 9, and lim f(x) exists.
X3"
x-3+
x--3
No, lim f(x) cannot exist if lim f(x) * lim f(x).
X3
X-3+
Transcribed Image Text:Explain what it means to say that lim f(x) = 7 x-3" lim f(x) = 9. and x+ 3* As x approaches 3, f(x) approaches 7, but f(3) = 9. %3! As x approaches 3 from the left, f(x) approaches 7. As x approaches 3 from the right, f(x) approaches 9. O As x approaches 3, f(x) approaches 9, but f(3) = 7. O As x approaches 3 from the right, f(x) approaches 7. As x approaches 3 from the left, f(x) approaches 9. In this situation is it possible that lim f(x) exists? Explain. O Yes, f(x) could have a hole at (3, 7) and be defined such that f(3) = 9. O Yes, f(x) could have a hole at (3, 9) and be defined such that f(3) = 7. O Yes, if f(x) has a vertical asymptote at x = 3, it can be defined such that lim f(x) = 7, lim f(x) = 9, and lim f(x) exists. X3" x-3+ x--3 No, lim f(x) cannot exist if lim f(x) * lim f(x). X3 X-3+
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