Solved: 4346 TrueFalse Determine whether the statement is true or false. Explain your
Chapter 1, Problem 46(choose chapter or problem)
Determine whether the statement is true or false. Explain your answer.
Suppose that \(M\) is a positive number and that for all real numbers \(x\), a function \(f\) satisfies
\(-\mathrm{M} \leqq \mathrm{f}(\mathrm{x}) \leqq \mathrm{M}\)
Then
\(\lim \limits_{x \rightarrow 0} x f(x)=0 \quad \text { and } \quad \lim \limits_{x \rightarrow+\infty} \frac{f(x)}{f}=0\)
Equation Transcription:
M
x
f
- M f(x)
M
= 0
= 0
Text Transcription:
M
x
f
-M leq f(x) leq M
lim_x right arrow 0 xf(x)
lim_x right arrow +infinity f(x)/f = 0
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