First slide
Continuity
Question

A function is defined as fx=limncos2nx,ifx<01+xnn,if0x111+xn,ifx>1which of the following does not hold good?

Moderate
Solution

f0-=limnlimn0-cos2xn=avaluelesserthan1=0f0+=limnlimn0+1+xn1n=1

Also, f(0) = 1. So, the function is discontinuous at x = 0.

Further,f1-=1;f1+=0;f1=1.

So, the function is discontinuous at x = 1.

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