Answered: Step 1 f(0)= x = 0 Sx2, x>0 Step 3 f(0)…

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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Answer the problem by following the steps, your answers must be followed by the steps I provided (Step 1-3, conclusion and illustration). Show your Complete Solutions in each Steps ( This is all about Continuity of a Function).

I already provided the answers I just need the COMPLETE SOLUTIONS in each steps (step 1-3) and the graph and conclusion. See answers in the picture I provided.

The function f(x) =
fx², x >0
1 x, xS0
is an example of a piecewise defined function.
Prove that this function is continuous or not on its entirety.
Step1: Evalucte the funcfion fctxxO at x-0
メx>0
Step 2: Find limix,x<o
Step 3: What did
you observe between the valves of fco) and limfox?
メ→○
Conclusion:
Illustrate the graph:

Step 1 f(0) = x = 0
x', x>0
x, x<0
Step 3 f(0) = lim
%3D
ポ→0
Conclusion: The function is continuous at x 0
x>0
Step 2 lim
X, x<0

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