Question

limit X approaches 0
1-cosx / x

Answer 1

you will have to apply La Hospital Rule

Answer 2

lol

Answer 3

actually you don't
what are you allowed to use for this?

Answer 4

my head

Answer 5

this become 0/0

Answer 6

hahaha

Answer 7

do you mean (1-cos x)/x or 1-(cosx)/x

Answer 8

Evaluate each of the following limits or show that they do not exist. Show Your work! limit x approach 0 ....(1-cosx)/(x) Trick question? just zero?

Answer 9

one way is to note that this is the negative of the derivative of cosine at \(x=0\)

Answer 10

another way is to recall in from your calc book that
\[\lim_{x\to 0}\frac{\cos(x)-1}{x}=0\]

Answer 11

it probably uses something called the "squeeze theorem" to prove it

Answer 12

it's lim sinx approach 0

Answer 13

Yea but we are not using infinitive limits

Answer 14

Unless they want me to use them to evaluate and prove? Idk its my last limit problem on my practice final and i just want to put 1-1 / 0 = 0/0 but i think that would be wrong

Answer 15

So... DNE i suppose

Answer 16

maann just use l'hospital rules why get so complicated xD

Answer 17

http://www.youtube.com/watch?v=vNtJ87U8G3I that can be helpful

Answer 18

haha well thats convenient

Answer 19

i don't want to break the rules ,and i want to help so.......^_^

Answer 20

whats breaking the rules?

Answer 21

the forum code

Answer 22

http://www.youtube.com/watch?v=igJdDN-DPgA watch this too its the squeeze theorm on how sin x / x = 1

Answer 23

it is not complicated at all
l'hopitals rule for this is inappropriate because i am going to guess that this comes way before l'hopital, and maybe even before differentiation

Answer 24

the limit is 0, not "DNE"

Answer 25

one easy way to find it would be to graph
\[y=\frac{1-\cos(x)}{x}\] and you would see that at \(0\) it is zero

Answer 26

Haha I see, I think l'hopital would work though i recognize learning it at one point, just dont remmeber it quite well, i remmeber there was a lot of situations it didnt work so i threw it out the window i think