3a+7T-スO Find lim f(2) . Do not use· Do not use

Given function is fx=3x+7 if x<−1x2+3 if −1≤x<15x−1 if 1≤x. (a) We have to find the…

Answered: T-EB ) Find lim f(2). Do not use quep ל…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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3a+7
T-ス
O Find lim f(2) . Do not use
· Do not use

Expert Solution

Step 1

Given function is $f (x) = \{\begin{cases} 3 x + 7 i f x < - 1 \\ x^{2} + 3 i f - 1 \leq x < 1 \\ 5 x - 1 i f 1 \leq x \end{cases}$ .

(a) We have to find the $\lim_{x \to - 1} f (x)$ .

Left hand limit at $x = - 1$ is given by

$\begin{matrix} \lim_{x \to - 1^{-}} f (x) = \lim_{x \to - 1^{-}} (3 x + 7) \\ = 4 \end{matrix}$

Hence, $\lim_{x \to - 1^{-}} f (x) = 4$

Right hand limit at $x = - 1$ is given by

$\begin{matrix} \lim_{x \to - 1^{+}} f (x) = \lim_{x \to - 1^{+}} (x^{2} + 3) \\ = 4 \end{matrix}$

Hence, $\lim_{x \to - 1^{+}} f (x) = 4$

Hence at $x = - 1$ , limit of $f (x)$ is exist

And $\lim_{x \to - 1} f (x) = 4$

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