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Question

Check the continuity of 'f' given by
f(x)=⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪4x2ifx0x5if0<x14x29if1<x<23x+4ifx>2 at points x = 0, 1, 2 form

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Solution


at x = 0
f(0) = 4(0)2 = 4
limx0=4x2=402=4limx0=x5=05=5Since f(0)=limx0limx0tf(x)
f(x) is not continous at x = 0.

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