Question

Evaluate limit x-> infinity tanhx

Answer 1

I did sinhx / coshx = e^x - e^-x /e^x + e^-x
so that's the indeterminate form, but when i deferetiate again , the ans just keep rotating , never gives an actual number

Answer 2

e^x - e^-x /e^x + e^-x =( e^{2x} -1) / (e^{2x}+1)
now differentiate

Answer 3

still dont know..infinity - 1 / infinity +1

Answer 4

what u don't know ?

Answer 5

ohhh

Answer 6

infinity - 1 / infinity +1 = inf/inf
so u can use L'Hopital's rule

Answer 7

limti is 1

Answer 8

thats correct!

Answer 9

yep, i got it thanks!

Answer 10

welcome ^_^

Answer 11

@hartnn sorry i have one more question. i got 2e^2x / 2e^2x , so if x -> - infinity, wouldn't the limit be 1 also since they just cancel out?

Answer 12

yes! ofcourse.

Answer 13

but my answer key says is -1

Answer 14

let me think...

Answer 15

it is totally possible that the answer key make a mistake too

Answer 16

its -1
i would do it like this :
limit x-> -infinity tanhx
put x=-x to get
limit x-> infinity tanh(-x) = -tanh x
so u get -1

Answer 17

oh ok thanks