Question

how to solve this limit stepwise? lim(x-->infinity) 2e^x+3e^-x/5e^x-7e^-x

Answer 1

multiply by\[{e^{-x}\over e^{-x}}\]then evaluate

Answer 2

I don't get it

Answer 3

what do you get after that multiplication?

Answer 4

2e^x(e^-x)+4e^-x/5e^x-8e^-x

Answer 5

no, that is not\[{2e^x+4e^{-x}\over5e^x-8e^{-x}}\cdot{e^{-x}\over e^{-x}}\]check your algebra

and also, how do you simplify \(e^x\cdot e^{-x}\) ?

Answer 6

1?

Answer 7

so it's 2+4e^-x/5-8e^-x
which gives u 2/5?

Answer 8

yes :)

Answer 9

thank you!!!!

Answer 10

welcome :)

Answer 11

i suck at limits :(

Answer 12

btw it should be \(e^{-2x}\) after multiplication, but that didn't matter since those terms vanish anyway

limits' like all things, come with practice
once you've seen all the tricks, you'll get used to it :)

Answer 13

^ the \(4e^{-2x}\) part I meant
(since \(e^{-x}\cdot e^{-x}=e^{-2x}\))

Answer 14

thank you! :)