## Brooke_army Group Title Evaluate the following limit: lim (1+7/x)^x/12 x→∞ one year ago one year ago

1. Brooke_army Group Title

I got the number 0.583

2. Brooke_army Group Title

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

3. hartnn Group Title

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

4. mathmate Group Title

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

5. Brooke_army Group Title

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

6. Brooke_army Group Title

mathmate it's the second

7. abb0t Group Title

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

8. Brooke_army Group Title

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

9. Brooke_army Group Title

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

10. abb0t Group Title

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

11. hartnn Group Title

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

12. hartnn Group Title

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

13. hartnn Group Title

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

14. Brooke_army Group Title

im trying that right now

15. hartnn Group Title