Question

limit as x approaches 0 of cos(1/x) ? can someone show me the work , I know it is undefined, but why?

Answer 1

Because you have a 0 in the denominator, and when you have a 0 in the numerator, you can get a 0 as an answer but when it's in the denominator (like here) it would be undefined.

Answer 2

but I was thinking because the cos(1/x) with zero as the denominator would make it cos(0) which is 1. so I'm confused.

Answer 3

Nooo, anything with a 0 in the denominator is undefined. But since you are taking the limit as x approaches 0, at not exactly at 0, you can plug in values for x that are really, really close to 0 (i.e. 0.001, 0.0001 etc) and see what you get.

when I plugged in x=0.001, I came out with 0.56 (which is positive), but when I plugged in x=0.0001, I got -0.95 (which is negative)... and since you are getting closer to 0 and the y-values are changing so rapidly, the limit doesn't exist?

Answer 4

But one thing for sure. Cos (1/0) does NOT equal Cos (0) because anything over 0 is undefined.

Answer 5

okay thank you!

Answer 6

yw :)