Continuity and limits with transcendental functions: Determine the interval on w

Kye

Kye

Answered question

2021-10-31

Continuity and limits with transcendental functions: Determine the interval on which following functions
f(x)=ex1ex

Answer & Explanation

lobeflepnoumni

lobeflepnoumni

Skilled2021-11-01Added 99 answers

Given 
f(x)=ex1ex 
With the exception of the point where the denominator equals 0, f(x) is continuous at all other points
1ex=0 
ex=1 
lnex=ln1 
x=0 
Intervals of continuity are therefore
(,0) and (0,) 
limx0f(x)=limx0ex1ex 
=limh0eh1eh 
=limh01(eh1h)h 
=limh01h 
= 
limx0+f(x)=limx0+ex1ex 
=limh0eh(eh1) 
=limh0eh(eh1h)h 
=limh0(ehh) 
=

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