Solution Found!
3136 Use Definition 1.4.1 to prove that the stated limit iscorrect. In each case, to
Chapter 1, Problem 35(choose chapter or problem)
Use Definition 1.4.1 to prove that the stated limit is correct. In each case, to show that \(\lim _{x \rightarrow a} f(x)=L\), factor \(|f(x)-L|\) in the form
\(|f(x)-L|=\mid \text { "something }^{\prime \prime}|\cdot| x-a \mid\)
and then bound the size of |”something"| by putting restrictions on the size of \(\delta\)
\(\lim _{x \rightarrow 4} \sqrt{x}=2\)
Equation Transcription:
Text Transcription:
lim_x rightarrow a f(x) = L
|f(x)-L|
|f(x)-L|=|"something"| times |x-a|
delta
lim_x rightarrow 4 sqrt x = 2
Questions & Answers
QUESTION:
Use Definition 1.4.1 to prove that the stated limit is correct. In each case, to show that \(\lim _{x \rightarrow a} f(x)=L\), factor \(|f(x)-L|\) in the form
\(|f(x)-L|=\mid \text { "something }^{\prime \prime}|\cdot| x-a \mid\)
and then bound the size of |”something"| by putting restrictions on the size of \(\delta\)
\(\lim _{x \rightarrow 4} \sqrt{x}=2\)
Equation Transcription:
Text Transcription:
lim_x rightarrow a f(x) = L
|f(x)-L|
|f(x)-L|=|"something"| times |x-a|
delta
lim_x rightarrow 4 sqrt x = 2
ANSWER:Step 1 of 3
Consider any arbitrary ,
By multiplying and dividing by , we get