Help solve step by step Use the graph of y= f(x)C-value toy=f(x)and the giverfind the following, wheneverthey exist. ( s infinite,If the imitisenter o∞ orasappropriate. If the limmit doesnot otherwiße exist, enter ONE,)C=-4,53X--3Y=f(x)Im fG)=lim F(x)=lim f(x)=X->Cf(() =

Answered: graph of y= tx) C-value to and the To…

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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Help solve step by step

Use the graph of y= f(x)
C-value to
y=f(x)
and the giver
find the following, whenever
they exist. ( s infinite,
If the imitis
enter o∞ or
as
appropriate. If the limmit does
not otherwiße exist, enter ONE,)
C=-4,5
3
X-
-3
Y=f(x)
Im fG)=
lim F(x)=
lim f(x)=
X->C
f(() =

Expert Solution

Step 1

Note that the given function is discontinuous at (x, y) = (-4, 5). So, the graph of the function has two points 1) x<-4
and 2) >-4.

Now, suppose we are travelling on the x-axis. Then from the graph we can see that as we tend to wards x = -4, from the left side, the value of y approaches y = 5.
Thus, $\lim_{x \to c^{-}} f (x) = 5$ .

Next, we travel along the x axis, towards the point x = -4, from the right side. Then we see that the value of the function approaches to y = -6.
Thus, $\lim_{x \to c^{+}} f (x) = - 6$

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