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
http://tinypic.com/r/2ikllf/7
http://tinypic.com/r/2mo1mrs/7
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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.
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.
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At x = 2 it is discontinuous because f(x) as x -->2- and f(x) as x -->2+ differ.