Question

LIMITS AN . Check the continuity of f given by (x²-4). if 02​

Answer 1

4−x

2

x−5

4x

2

−9

3x+4

x≤0

0<x≤1

1<x<2

x≥2

at the points 0,1 and 2.

Medium

Solution

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For the point x=0

RHL=

x→0

lim

4−x

2

=4

LHL=

x→0

lim

x−5=−5 As, LHL



=RHL it is not continuous at x=0

For the point x=1

RHL=

x→1

lim

4x

2

−9=−5

LHL=

x→1

lim

x−5=−4 as, LHL



=RHL it is not continuous at x=1

For the point x=2

RHL=

x→2

lim

3x+4=10

LHL=

x→2

lim

4x

2

−9=7 as, LHL



=RHL it is not continuous at x=2