Question

Check Continuity of f(x)= x^2 - 4/x-2

at x=2​

Answer 1

Answer:

f(x)=

⎩

⎪

⎪

⎨

⎪

⎪

⎧

2

x

2

−4

,if0<x<2

0ifx=2

2−8x

3

ifx>2

⎭

⎪

⎪

⎬

⎪

⎪

⎫

⇒f(2)=0

lim

x→2

f(2)=lim

x→2

f(2−h)=lim

x→2

2

(2−h)

2

−4=lim

x→2

2

h−4+h

2

−4

lim

x→2

2

k

2

−4h

=0

lim

x→2

f(2

+

)=lim

x→2

f(2+h)=lim

x→2

2−

(2+h)

3

8

=lim

x→2

(2+h)

3

2(8+12h+6h

2

+h

3

)

lim

x→2

(2+h)

3

16+24h+2h

2

+2h

3

−8

=2lim

x→2

(2+h)

3

(4+12h+6h

2

+h

3

)

=∴f(2

−

)



=f(2

)

It is discontinuous

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

f(x)=x^2-4/x-2

f(2)=(2)^2-4/2-2

=4-4/0

here anything by zero is infinity.

so there is no continuity

hope my answer helps you