2. Suppose DC R and functions f: D→ R and g: DR. Suppose to is an accumulation point of D and lim f(x) = A all lim g(x)=B both exist (except in last part below). H-10 (a) Show that lim f(x) g(x) = AB, using the definition. HIHO (b) Show that lim f(x)g(x) = AB, using sequences. X-10 01 x (c) Give an example to show that lim f(x) g(x) may exist even though both lim f(x) and lim g(x) do not exist. HIO I-IO HIHO
2. Suppose DC R and functions f: D→ R and g: DR. Suppose to is an accumulation point of D and lim f(x) = A all lim g(x)=B both exist (except in last part below). H-10 (a) Show that lim f(x) g(x) = AB, using the definition. HIHO (b) Show that lim f(x)g(x) = AB, using sequences. X-10 01 x (c) Give an example to show that lim f(x) g(x) may exist even though both lim f(x) and lim g(x) do not exist. HIO I-IO HIHO
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.1: Concept Of A Function
Problem 100PS
Related questions
Question
![2. Suppose DCR and functions f: DR and g: DR. Suppose to is an accumulation point of D and lim f(x) = A anc
xx0
lim g(x)= B both exist (except in last part below).
I-IO
(a) Show that lim f(x) g(x) = AB, using the definition.
xx0
(b) Show that lim f(x)g(x) = AB, using sequences.
x xo
(c) Give an example to show that lim f(x) g(x) may exist even though both lim f(x) and lim g(x) do not exist.
x-x0
x-xo
x x0
idon the function of fractiona](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd597ffd2-5c4b-4c2e-8332-77ce1607dac1%2Fa7c02c07-84c1-4f94-b6b0-60b8cb60e3be%2Fiiypi7j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Suppose DCR and functions f: DR and g: DR. Suppose to is an accumulation point of D and lim f(x) = A anc
xx0
lim g(x)= B both exist (except in last part below).
I-IO
(a) Show that lim f(x) g(x) = AB, using the definition.
xx0
(b) Show that lim f(x)g(x) = AB, using sequences.
x xo
(c) Give an example to show that lim f(x) g(x) may exist even though both lim f(x) and lim g(x) do not exist.
x-x0
x-xo
x x0
idon the function of fractiona
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