1
Question
Let f(x)=ā§āØā©x1+e1/x xā 0,0 x=0. Then
Let f(x)=ā§āØā©x1+e1/x xā 0,0 x=0. Then
Open in App
Solution
The correct options are
B f′(0−)=1
C f′(0+)=0
We know that,
f′(0−)=limx→0−f(x)−f(0)x⇒f′(0−)=limh→0+f(−h)−f(0)−h⇒f′(0−)=limh→0+−h1+e−1/h−h⇒f′(0−)=limh→0+11+e−1/h=1
And
f′(0+)=limx→0+f(x)−f(0)x⇒f′(0+)=limh→0+f(h)−f(0)h⇒f′(0+)=limh→0+h1+e1/hh⇒f′(0+)=limh→0+11+e1/h=0
B f′(0−)=1
C f′(0+)=0
We know that,
f′(0−)=limx→0−f(x)−f(0)x⇒f′(0−)=limh→0+f(−h)−f(0)−h⇒f′(0−)=limh→0+−h1+e−1/h−h⇒f′(0−)=limh→0+11+e−1/h=1
And
f′(0+)=limx→0+f(x)−f(0)x⇒f′(0+)=limh→0+f(h)−f(0)h⇒f′(0+)=limh→0+h1+e1/hh⇒f′(0+)=limh→0+11+e1/h=0
Suggest Corrections
0
Similar questions
View More
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
