Explain why or why not Determine whether the followingstatements are true and give an explanation or counterexample.Assume a and L are finite numbers. a. If lim f(x) = L, then f(a) = L.b. If lim f(x) = L, then lim f(x) = L.c. If lim f(x) = L and lim g(x) = L, then f(a)= 8(a).f(x) adoes not exist if g(a) = 0.d. The limit lima g(x)e. If lim Vf(x)lim f(x), it follows thatlim Vf(x)lim f(x).%3D

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Description: Explain why or why not Determine whether the followingstatements are true and give an explanation or counterexample.Assume a and L are finite numbers. a. If lim f(x) = L, then f(a) = L.b. If lim f(x) = L, then lim f(x) = L.c. If lim f(x) = L and lim

Part (a) Given If limx→afx=L then fa=L

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a. If lim f(x) = L, then f(a) = L. b. If lim f(x) = L, then lim f(x) = L. c. If lim f(x) = L and lim g(x) = L, then f(a) = 8(a). f(x) a does not exist if g(a) = 0. d. The limit lim a g(x) e. If lim Vf(x) lim f(x), it follows that lim Vf(x) lim f(x). %3D

a. If lim f(x) = L, then f(a) = L. b. If lim f(x) = L, then lim f(x) = L. c. If lim f(x) = L and lim g(x) = L, then f(a) = 8(a). f(x) a does not exist if g(a) = 0. d. The limit lim a g(x) e. If lim Vf(x) lim f(x), it follows that lim Vf(x) lim f(x). %3D

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

Topic Video

Question

Explain why or why not Determine whether the following
statements are true and give an explanation or counterexample.
Assume a and L are finite numbers.

a. If lim f(x) = L, then f(a) = L.
b. If lim f(x) = L, then lim f(x) = L.
c. If lim f(x) = L and lim g(x) = L, then f(a)
= 8(a).
f(x) a
does not exist if g(a) = 0.
d. The limit lim
a g(x)
e. If lim Vf(x)
lim f(x), it follows that
lim Vf(x)
lim f(x).
%3D

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