## anonymous 3 years ago Evaluate the following limit: lim (1+7/x)^x/12 x→∞

1. anonymous

I got the number 0.583

2. anonymous

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

3. hartnn

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

4. mathmate

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

5. anonymous

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. anonymous

mathmate it's the second

7. abb0t

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

8. anonymous

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

9. anonymous

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

10. abb0t

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

11. hartnn

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

12. hartnn

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

13. hartnn

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. anonymous

im trying that right now

15. hartnn

16. anonymous

thanks i got the right answer

17. hartnn

good! you're welcome ^_^