Show limitations. See image Let fo Cx)=iう 0K×S 4C.(x-4)+2 ifわxv4- where C denates a real constant.Show thatlim fc (x) = Lim fclx)and%3Dtc15 continuous at X=4 tor any real c,

The function fcx=x, if 0≤x≤4cx-4+2 if x>4. Where c is a real constant. We have to…

Answered: Let fc Cx)= Vx if osxs 4 c.(x-4)+2 if…

Let fc Cx)= Vx if osxs 4 c.(x-4)+2 if x>4 denotes a real constant. - where C Show that lim fe (x) = limfelx) %3D and fc is continuous at x=4for any realc ,

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.5: Solution Of Cubic And Quartic Equations By Formulas (optional)

Problem 32E

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Question

Show limitations. See image

Let fo Cx)=
iう 0K×S 4
C.(x-4)+2 ifわxv4
- where C denates a real constant.
Show that
lim fc (x) = Lim fclx)
and
%3D
tc15 continuous at X=4 tor any real c,

Expert Solution

Step 1: Given,

The function $f_{c} (x) = \{\begin{cases} \sqrt{x}, i f 0 \leq x \leq 4 \\ c (x - 4) + 2 i f x > 4 \end{cases} .$ Where c is a real constant. We have to show that

$\lim_{x \to 4^{+}} f_{c} (x) = \lim_{x \to 4^{-}} f_{c} (x)$

and the function is continuous at x = 4 for any real number.

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