Question

limit as x approaches negative infinity
of the following function
(cos(4x))/x

Answer 1

without a calculator, how do I know the solution is 0?

Answer 2

can I break it up as 1/x and cos(4x)

Answer 3

when x approaches +infinity or -infinity
what values can cos take ?

yes, you can do that

Answer 4

it oscillates, I think

Answer 5

between ?

Answer 6

0 because 0 is it midline (if my memory serves me)

Answer 7

it oscillates between -1 and +1 right ?
it will take finite values in this interval only, its bounded, right ?

Answer 8

sorry, it has been a long time...

Answer 9

n,
so lim x-> -infty 1/x = 0
and 0 times (ANY value between -1 to +1) is 0 only.

Answer 10

i meant, np, no problem :)

Answer 11

Thanks :)

Answer 12

you're welcome ^_^