Determine limit as x approaches 0?

Im quite stuck on one question in my most recent assignment, where it asks me to :

Determine :

I'm confused to as to what the question is asking me/ where i should start(never really understood limits)
? I dont want anyone to walk me through it, but if someone could point me in the right direction it would be appreciated

Reply 1

DFranklin

18

I would use the taylor series for cos x here.

Reply 2

santeria133

OP

Original post by DFranklin

I would use the taylor series for cos x here.

Alright so my problem is i dont know where the rest of the equation fits in? what would i do with the x^2/2 and the x^4 ? I'm assuming the x^4 means that i expand the series to the 4th term?

Reply 3

brianeverit

9

Original post by santeria133

Alright so my problem is i dont know where the rest of the equation fits in? what would i do with the x^2/2 and the x^4 ? I'm assuming the x^4 means that i expand the series to the 4th term?

and then divide the result by the x^4 in the denominator

Reply 4

lubus

12

Keep applying L'Hopitals rule.

Reply 5

davros

16

Original post by lubus

Keep applying L'Hopitals rule.

The Taylor series approach is much simpler :smile:

Reply 6

BlueSam3

17

Original post by santeria133

Im quite stuck on one question in my most recent assignment, where it asks me to :

Determine :

I'm confused to as to what the question is asking me/ where i should start(never really understood limits)
? I dont want anyone to walk me through it, but if someone could point me in the right direction it would be appreciated

Bound the function.

(edited 10 years ago)

Reply 7

ztibor

10

Original post by santeria133

Im quite stuck on one question in my most recent assignment, where it asks me to :

Determine :

I'm confused to as to what the question is asking me/ where i should start(never really understood limits)
? I dont want anyone to walk me through it, but if someone could point me in the right direction it would be appreciated

While the limit of both the numerator and denominator is 0, you can use the
L'Hospital rule (3 times),then use that

\lim_{x \rightarrow 0} \frac{\sin x}{x}=1

Determine limit as x approaches 0?

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