(a) Prove that if then (Note: This is the converse of Exercise 112.) (b) Prove that if
Chapter 1, Problem 114(choose chapter or problem)
(a) Prove that if \(\lim \limits_{x \rightarrow c}|f(x)|=0\), then \(\lim \limits_{x \rightarrow c} f(x)=0\).
(Note: This is the converse of Exercise 112.)
(b) Prove that if \(\lim \limits_{x \rightarrow c} f(x)=L\), then \(\lim \limits_{x \rightarrow c}|f(x)|=|L|\).
[Hint: Use the inequality \(\|f(x)|-| L\| \leq|f(x)-L|\).]
Text Transcription:
lim_x rightarrow c |f(x)| = 0
lim_x rightarrow c f(x) = 0
lim_x rightarrow c f(x) = L
lim_x rightarrow c |f(x)| = |L|
||f(x) - L|| leq |f(x) = L|
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