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Question

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

A
continuous and derivable at x=1
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B
neither continuous nor derivable at x=1
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C
continuous but not derivable at x=1
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D
none of these
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Solution

The correct option is B neither continuous nor derivable at x=1
For x1, we have
f(x)=12x+3x24x3+...=(1+x)2=(11+x)2
Now, limx1f(x)=limx11(1+x)2= f(x)is not continous at x=1
So, f(x) is not derivable at x=1
Hence f(x) is neither continuous nor derivable at x=1

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