Question

Evaluate the following limit:
lim (1+7/x)^x/12
x→∞

Answer 1

I got the number 0.583

Answer 2

the correct answer is 1.79.
I'm not sure where i went wrong

Answer 3

how did you get 0.583 ? mind showing your work/steps ?

Answer 4

is it \( \large \frac{(1+7/x)^x}{12}\) or \( \large (1+7/x)^{x/12} \)

Answer 5

y=lim (1+7/x)^x/12
ln(y)=lim x/12 ln(1+7/x)
\[\frac{ \ln(1+\frac{ 7 }{x} }{\frac{12 }x }\]

Answer 6

mathmate it's the second

Answer 7

\[\lim_{x \rightarrow ∞} \frac{ (1+7)^x }{ 12 }\]

Answer 8

then i took d/dx to both the numerator and the denominator

Answer 9

the problem is
\[\lim_{x \rightarrow \infty} (1+\frac{ 7 }{ 12})^\frac{ x }{12 }\]

Answer 10

In order to use L'hopitals rule, you must have a fraction with a function on the numerator and denominator

Answer 11

do you know a general formula
\[\lim_{y \rightarrow 0} (1+y)^{\frac{ 1}{y}}=...?\]

Answer 12

if you know ^ that, then you can put 7/x = y
in your limit question first, to bring in that form.

Answer 13

if you use the formula, you get the correct answer in just few steps by adjusting the exponent.
\[\lim_{y \rightarrow 0} (1+y)^{\frac{ 1}{y}}=e\]

Answer 14

im trying that right now

Answer 15

okay :) take your time...

Answer 16

thanks i got the right answer

Answer 17

good! you're welcome ^_^