f(x) = {x+2,x not equal to 1
0,2=1
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Step-by-step explanation:
Is f(x) = (1 + x) ^1 /x, when x is not equal to 0 and f(x) = e, when x=0, continuous at x=0?
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2 Answers

Muhammad Abul Fazal, B.Sc. (Hons.) Mathematical Physics, University of Alberta (2022)
Answered May 8, 2018
Lets see if it is;
f(0)=ef(0)=e
If x≠0x≠0
limx→0(1+x)1xlimx→0(1+x)1x
Now if 1x→0⇒x→∞1x→0⇒x→∞
Therefore Limit can be modified as:
limx→∞(1+1x)x=elimx→∞(1+1x)x=e
(This limit is definition of ´e´)´e´)
Concluding:
limx→0f(x)=f(0)limx→0f(x)=f(0)
Hence function is continuous on x=0x=0.
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