Thread: limit help please!!

how do i prove lim (x^2) * (cos(1/x)) = 0
as x approaches 0
please can you list the steps

Note that cos(1/x) is bounded, no matter how rapidly it oscilates when x is near 0. Then apply the squeeze theorem.

Originally Posted by johnsomeone

Note that cos(1/x) is bounded, no matter how rapidly it oscilates when x is near 0. Then apply the squeeze theorem.

Or just the fact that the product of a function that goes to 0 with a bounded function is 0.

ok then how do i prove it on a 10 point free response question. can someone please list out the steps so that i can understand for future tests because i only got 3/10 for this question on the test

Originally Posted by ubhutto

ok then how do i prove it on a 10 point free response question. can someone please list out the steps so that i can understand for future tests because i only got 3/10 for this question on the test

thus

Both .