Question

How do you find the lim x-> ∞ of tan(π/4cos(sin x^1/3))? Please be thorough thanks!

Answer 1

The function is this?

\[\tan\left( \pi/4 . \cos(\sin(x^{1/3})) \right)\]

Answer 2

yes

Answer 3

Then think about whether or not
sin(x^{1/3}) has a limit as x --> infinity

Remember that sin oscillates without end.

Answer 4

the limit does not exist as x-> infinity for sin (x^1/3)\[\sin x^{1/3}\]

Answer 5

Right. Hence does your function have a limit as x --> infinity ?

Answer 6

I'm going to say no

Answer 7

And you'd be right.