Question

f(x) = {x+2,x not equal to 1
0,2=1

Answer 1

Answer:

Understand

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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