Question

Infinite limits with exponential functions.

Answer 1

\[\frac{ 1-e^x }{ 1+2e^x }\]

Answer 2

lim x-> inf

Answer 3

divide numerator and denominator by e^x

Answer 4

what do you get ?

Answer 5

ok, so i know when e^x x-> inf, that it = inifinity

Answer 6

take out e^x as a common factor in both numerator and denominator..

Answer 7

?

Answer 8

that will give me a 0 in the num

Answer 9

\[\frac{ 1-\infty }{ 1+2(\infty )}\]

Answer 10

\[\frac{ \frac{ 1 }{ e^x } - \frac{ e^x }{ e^x }}{ \frac{ 1 }{ e^x } + \frac{ 2e^x }{ e } }\]

Answer 11

if you divide numerator and denominator by e^x this is what you get .

Answer 12

so multiply top and bottom 1/e^x

Answer 13

\[\frac{ \frac{ 1 }{ e^x } - 1 }{ \frac{ 1 }{ e^x } + 2 }\]

Answer 14

after simplifying this what you have..
so what is the limit now ?

Answer 15

hang on not sure how to simplify that

Answer 16

what i wrote there is after the simplification of the division of num and denom by e^x..

Answer 17

ya, not sure how to get rid of 1/e^x

Answer 18

1/e^x = 1/infinty = 0 as limit tends to infinty

Answer 19

ahhhhh!

Answer 20

thanks @AbhimanyuPudi

Answer 21

just as 1/x = zero

Answer 22

wouldn't you use the Powers rule?
\[\frac{ (1-e^x) }{ (1+2e^x) }\]

e^x has the power of 1 on the top
2e^x has the power of 2 on the bottom

The answer is 1/2

Answer 23

its -1/2

Answer 24

yeah that lol

Answer 25

-0.5 indeed

Answer 26

welcome @Calle87