Question
Asked Sep 25, 2019
1 views
Find the limit.
1 t1
5
lim 4e 4
1t
t 0
t
t
LC
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Find the limit. 1 t1 5 lim 4e 4 1t t 0 t t LC

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Expert Answer

Step 1

First we take the limit inside and simplify

4e'-4 +t -1
lim
t
5
1+t
1+t -1
4e-4
5
lim
lim
lim
1+t
t
t 0
t
t 0
t 0
)
1+t -1
5
lim
1
lim
lim
1+t
t 0
t
t0
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4e'-4 +t -1 lim t 5 1+t 1+t -1 4e-4 5 lim lim lim 1+t t t 0 t t 0 t 0 ) 1+t -1 5 lim 1 lim lim 1+t t 0 t t0

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Step 2

For first and second term we get 0/0 form. So we use L'hopitals...

VI+t -
lim
4 lim
lim
1+t
t 0
t
t 0
t0
1
2V1+t
5
, lim
4 lim
1
1+0
t 0
t 0
(
1
(4 lim(e)lim
2V1+t
t 0
t0
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VI+t - lim 4 lim lim 1+t t 0 t t 0 t0 1 2V1+t 5 , lim 4 lim 1 1+0 t 0 t 0 ( 1 (4 lim(e)lim 2V1+t t 0 t0

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