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what is the limit of this equation?
I know that it is convergent but i can not solve it to find the limit.
lim (n → infinity ) an of
7n
____
n+7
4 Answers
- PaulR2Lv 78 years agoFavorite Answer
limit n -> oo : ( ( 7n ) / ( n + 7 ) )
Break apart
limit n -> oo : ( ( 7n + 49 ) / ( n + 7 ) ) - ( ( 49 ) / ( n + 7 ) )
Divide
limit n -> oo : ( 7 ) - ( ( 49 ) / ( n + 7 ) )
Plug in oo
limit n -> oo : ( 7 ) - ( ( 49 ) / ( oo + 7 ) )
Add
limit n -> oo : ( 7 ) - ( ( 49 ) / ( oo ) )
Divide
limit n -> oo : ( 7 ) - 0
Subtract
limit n -> oo : 7
I hope this helps you. Have a good day.
- 8 years ago
7n / (n + 7) =>
(7n + 49 - 49) / (n + 7) =>
(7n + 49) / (n + 7) - 49 / (n + 7) =>
7 * (n + 7) / (n + 7) - 49 / (n + 7) =>
7 - 49/(n + 7)
n goes to infinity
7 - 49/inf =>
7 - 0 =>
7
The limit is 7
- ?Lv 78 years ago
I'm not at all sure what you mean by the "an" after the bracket lim(n ---> inf), but in the expression you have, divide top & bottom by n to get 7/(1 + 7/n) so as n---> inf, 7/n ---> 0 so the limit is 7/1 = 7
Source(s): Retired Maths Teacher - ?Lv 78 years ago
two thoughts as to how to approach this...
pick a big number x = 1000
f(1000) = 7000 / 1007 ~ 7
more rigorously.
z = 1/n
lim 7 (1/z)/(1/z + z)
as z approaches zero
multiply top and bottom by z
lim 7 / (1+z^2)
as z approaches zero.
7
