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Question

Show that the function f(x)=3x,ifx<12,ifx=11+x,ifx>1 is continuous at x=1

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Solution

limh0f(1h)=31+h=2+h=2
limh0f(1+h)=1+1+h=2+h=2
lim0f(1h)=f(1)=limh0f(1+h)
Hence the function is continuous at x=1.

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