limit e power X minus e power minus X over sin x
Answers
Answered by
1
Step-by-step explanation:
Given,
x→0
lim
(
2(x−sin(x))
e
x
−e
sin(x)
)
=
2
1
⋅
x→0
lim
(
x−sin(x)
e
x
−e
sin(x)
)
Apply L-Hospital's rule
=
2
1
⋅
x→0
lim
(
1−cos(x)
e
x
−e
sin(x)
cos(x)
)
=
2
1
⋅
x→0
lim
(
sin(x)
e
x
−e
sin(x)
(cos
2
(x)−sin(x))
)
Apply L-Hospital's rule
=
2
1
⋅
x→0
lim
(
cos(x)
2
3e
sin(x)
sin(2x)+2e
x
−2e
sin(x)
cos
3
(x)+2e
sin(x)
cos(x)
)
=
2
1
⋅
x→0
lim
(
2cos(x)
3e
sin(x)
sin(2x)+2e
x
−2e
sin(x)
cos
3
(x)+2e
sin(x)
cos(x)
)
=
2
1
⋅
2cos(0)
3e
sin(0)
sin(2⋅0)+2e
0
−2e
sin(0)
cos
3
(0)+2e
sin(0)
cos(0)
=
2
1
Answered by
1
Lt (e^x-e^-x)/Sinx
x→0
Lt
x→0. (e^x-1)/Sinx - (e^-x -1)/Sinx
Lt. (e^x-1)/x/Sinx/x - Lt. (e^-x-1)/-x/Sinx/-x
x→0. x→0
=1+1=2
Similar questions