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Question

For the function f(x)={x25,x3x+13,x>3


Consider the following statements:
1.The function is discontinuous at x=3.
2.The function is not differentiable at x=0.
Then which of the above statement(s) is correct:

A
1 only
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B
2 only
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C
Both 1 and 2
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D
Neither 1 nor 2
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Solution

The correct option is D Neither 1 nor 2
Given : f(x)={x25,x3x+13,x>3

Continuity at x=3
limx3f(x)=limx3(x25)=95=4limx3+f(x)=limx3+x+13=16=4L.H.L.=R.H.L.=f(3)
It is continuous at x=3

f(x)=x25, x3f(x)=2x, x<3
So the function f(x) is differentiable at x=0.
So, both statements are incorrect.

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