lim theta---0 costheta-1/theta

Question

lim theta--->0  costheta-1/theta

laddiusmaximus · Answer

i thought I would use 0.0001 and plug it in, but im not sure.

jamesj · Answer

No.  Have you learnt the derivative of cos(t) yet?

laddiusmaximus · Answer

no what is it?

jamesj · Answer

I can tell you with 100% certainty that this limit is zero.

I'm not sure exactly where you are in your education and why your teacher would set this problem right now.  But I'm guessing she wants you to think about the tangent to the graph of the function cos(theta).  Draw that graph and look at what the limit means geometrically on the graph.  You'll see that zero is the intuitive answer to the limit as well.

jamesj · Answer

[
If you had learnt the derivative of cos(t), then I would tell you that this limit is the negative of d/dt of cos(t) evaluated at t = 0, namely -sin(0) = 0.  But that is probably gibberish to you right now.
]