Please show steps for solving this function. Thanks in advance '2x2 - 4, x < 22 < x < 5x 2 5Determine the values for x for which the function f(x) ]x| =x + 2,is discontinuous.7,

Answered: (2x² – 4, x < 2 x + 2, 7, Determine the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please show steps for solving this function. Thanks in advance

'2x2 - 4, x < 2
2 < x < 5
x 2 5
Determine the values for x for which the function f(x) ]x| =
x + 2,
is discontinuous.
7,

Expert Solution

Step 1

For discontinuous, left hand limit and right hand limit should not be equal.

Step 2

For the function to be continuous at $x = 2$ ,

$\begin{array}{rcl} \lim_{x \to 2^{-}} f (x) & = & \lim_{x \to 2^{+}} f (x) \\ \lim_{x \to 2} (2 x^{2} - 4) & = & \lim_{x \to 2} (x + 2) \\ 2 {(2)}^{2} - 4 & = & 2 + 2 \\ 4 & = & 4 \end{array}$

As the equation is true, the function is continuous at $x = 2$ .

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