3136 Use Definition 1.4.1 to prove that the stated limit iscorrect. In each case, to

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 \(\delta\)

\(\lim _{x \rightarrow 1} 2 x^{2}=2\)[ Hint: Assume \(\delta \leq 1\). ]

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 1 2x^2 = 2

delta less than or equal to 1