lim x = 0. e^-x - e^-1/x-1
Answers
Answer:
Solution
It is a remarkable limit, but if you want to demonstrate ir, you have to know the fundamental limit:
x→∞
lim
(1+
x
1
)
x
=e (number of Neper), and also limit:
x→∞
lim
(1+x)
x
1
=e that it is easy to demonstrate in this way:
let x=
t
1
, so when x→0 than t→∞ and this limit becomes the first tone.
So,
let e
x
−1=t⇒e
x
=t+1⇒x=ln(t+1)
and if x→0⇒t→0
x→0
lim
x
e
x
−1
=
x→0
lim
ln(t+1)
t
=
x→0
lim
t
ln(t+1)
1
=
x→0
lim
t
1
ln(t+1)
1
=
x→0
lim
ln(t+1)
t
1
1
=
(for the seconf limit) =
lne
1
=
1
1
=1
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