Find the limit of the sequence or determine that the sequence diverges. <mroot> e

2d3vljtq 2022-07-12 Answered
Find the limit of the sequence or determine that the sequence diverges.
e 3 n + 4 n
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Answers (1)

Savion Stanton
Answered 2022-07-13 Author has 10 answers
Consider:
e 3 n + 4 n
Let y = ( e 3 n + 4 ) 1 n
Simplify this expression

So, ln ( y ) = ln ( ( e 3 n + 4 ) 1 n )
Apply the property of the logarithm function ln ( m n ) = n ln m
We get,
ln ( y ) = 1 n ln ( e 3 n + 4 )
Apply the limit
lim n ln ( y ) = lim n 1 n ln ( e 3 n + 4 )
ln ( y ) = lim n ( 1 n ln ( e 3 n + 4 ) )

After substituting limit we get the form of

Apply the L’hospital Rule
ln ( y ) = lim n ( 1 ( 3 ) e 3 n + 4 ( 1 ) )
= lim n ( 3 e 3 n + 4 )

Apply the limit
ln ( y ) = 3 e 3 ( ) + 4
= 3 e
= 0

Apply the rule of logarithm function ln m = n m = e n
Here m = y and n = 0
y = e 0
y = 1
Thus, the limit is 1

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