Question

find the limit as x->0 of cos(2x) / x
A) 1/2
B) 1
C) 2
D) cos 2
E) does not exist
I think the correct answer is E. but can you explain please why it is not or why it is? thanks c:

Answer 1

directly put x=0 , what do u get ?

Answer 2

DNE (:

Answer 3

Oh, u get 1/0 which is infinity.
do u know how to find left hand limit and right hand limit ?

Answer 4

wait i thought that 1/0 is dne?

Answer 5

limit will not exist when left limit does not equal right limit.
if they both are equal to 1/0 = infinity, then limit will exist and equals infinity.

Answer 6

u know how to find left and right limits ?

Answer 7

yes. they are equal. but infinity isnt one of my choices? unless i did it wrong :\

Answer 8

they are both equal to 1. i think.

Answer 9

on, nopes. left hand limit is when x-> 0-
that is x is very near to 0 but negative., hence u get -1/0 = -infinity as the value of limit.
but
right hand limit is when x-> 0+
that is x is very near to 0 but positive., hence u get 1/0 = infinity as the value of limit.
as these 2 are not equal, the limit DNE.
did u get this ??

Answer 10

oh! yes you are correct and i understand. i made a silly mistake and completely forgot about the x in the denominator. silly me :) thanks!

Answer 11

welcome :)