Calculus help... discontinuity & Intermediate Value Theorem
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Calculus help... discontinuity & Intermediate Value Theorem

[From: ] [author: ] [Date: 11-09-13] [Hit: ]
the limit does not exist and hence the function is not continuous.2.If f is continuous on [a, b] and L is a real number satisfying f(a) -At x = 2 it is discontinuous because f(x) as x -->2- and f(x) as x -->2+ differ.......
I can't get the right answers for these last two problem of my calc webwork. Answers for one or both will be much appreciated.

http://tinypic.com/r/2ikllf/7

http://tinypic.com/r/2mo1mrs/7

-
1.
The function is discontinuous at x = 2.

lim x -> 2- f(x)
= 2

lim x -> 2+ f(x)
= (2 - 1)^2
= 1

Since the limit from the left is not equal to limit from the right, the limit does not exist and hence the function is not continuous.

2.
A = 1 and B = 6

Intermediate value theorem:
If f is continuous on [a, b] and L is a real number satisfying f(a) < L < f(b), then there exists a point c between a and b where f(c) = L.

-
At x = 2 it is discontinuous because f(x) as x -->2- and f(x) as x -->2+ differ.
1
keywords: Intermediate,Theorem,discontinuity,help,Value,Calculus,amp,Calculus help... discontinuity & Intermediate Value Theorem
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