Question

lim x-> infinity cos^2(x)/x^2)

Answer 1

use taylor series for cosx

Answer 2

haven't learned it yet

Answer 3

in first few weeks of calc 1

Answer 4

well so intuition :
cos^2(x) as x-> 0 = 1 right ?

Answer 5

so it is like dividing 1 by 0 ..

Answer 6

note that if the x wasnt squared there would not be any limit
since for x->0+ and for x->0- you would get different answers.

Answer 7

Right

Answer 8

but since it is squared you have a limit..
what is your answer then ? :)

Answer 9

so that's it; it's just 0?

Answer 10

1/0 = 0 ?

Answer 11

No

Answer 12

so what is it then

Answer 13

if we evaluate the limit at 0 as it's written it comes to 1/0 no?

Answer 14

That's my issue; I'm not sure how to begin manipulating it to avoid that

Answer 15

yes.. so what is the answer

Answer 16

DNE?

Answer 17

does not exist

Answer 18

you divide a number by something really small.. you get infinity

Answer 19

okay, gotcha

Answer 20

thank you

Answer 21

yw