Activity 3 Continuity at a Point and on an Interval
f ( x) =
14. Given
x?2
x?3 ,
a. Is f ( x ) continuous at x = 2? Explain.
b. Is f ( x ) continuous at x = 3? Explain.
c. Find the interval(s) on which f ( x ) is continuous.
15. Find the interval(s) on which
g ( x) =
x+7
x 2 ? 49 is continuous.
3
?
? x + 3 x + 2 if x ? 0
h( x ) = ? 3
if x ? 0
?
?x
16. Given
h (0) =
lim h ( x )
lim h ( x )
Find: h (0) , x ?0?
and x ?0+
.
lim h ( x )
x ?0?
Is h ( x ) is continuous at x = 0? Explain.
=
lim h ( x )
x ?0+
=
2
3
Draw by hand the graph of h(x) from [-1, 2].
17. Determine the value of the constant T for which the function below is continuous
??(??) = {
?? 2 + 6?? + 5
,
??+5
?? < ?5 2???? ? 3,
?? ? ?5
4
18.
Find the points at which the function is discontinuous and determine whether the
discontinuity is removable or not, i.e. does the limit exist at the point of discontinuity?
x3 + x2 ? 2 x
g ( x) =
x ( x ? 2)
Point(s) of discontinuity
Removable or not? (Does the limit exist?)
Explain:

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