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Question

The function f(x)={12x+3x24x3+....,x11,x=1 is

A
Continuous at x=1
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B
Neither continuous nor differential at x=1
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C
differential at x=1
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D
not differential at x=1
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Solution

The correct options are
B not differential at x=1
C Neither continuous nor differential at x=1
For x1, we have
f(x)=12x+3x24x3+...=(1+x)1=11+x
limh0f(1h)=limh0111h
So, f(x) is not continuous at x=1
Also, limh0f(1h)f(1)(1h)(1)=limh01h1h=limh01+hh2
So, f(x) is not derivable at x=1
Hence, f(x) is neither continuous nor derivable at x=1

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