Question

Does the limit x-> infinity cos x exists?

Answer 1

or sin x or tan x

Answer 2

what are the possible values cos x can take ?

Answer 3

in other words, whats the range of cos x ?

Answer 4

I am not sure but I don't know if the limit exist

Answer 5

can't solve this the answer is 2

Answer 6

see, when x is a really large number, we say that
\(x \to \infty\)

and cos of x can be any finite number between -1 and 1,
because thats the range of cos

Answer 7

so you can reason out this way,

cos x/x

lim x-> infinity cos x will be a number between -1 to 1

lim x-> infinity 1/x = 0

so, limit x->infinity cos x/x = a finite numer times 0 = 0

Answer 8

your numerator then, will be just 2+0

Answer 9

and denominator is easily (1+0)^2 =1

as x->infinity, 1/x ->0
hence 2/x =0