Manus Domini

10-22-2011, 02:33 PM

Before I give the problem, I want posters to know I am NOT asking for the answer, so don't give it to me. Nor should you give away the entire process, because all I have to then do is plug in numbers, so you are giving me the answer anyway. I just want where to start and to be let known if I am doing the problem incorrectly.

So, the problem I am assigned is:

"analytically simplify the following limit, which represents the definition of the derivative f'(a) for the function f(x)=sinx and x=a."

My teacher doesn't give the limit, and so I don't know where to start. The substitute (since the teacher wasn't there yesterday) said something about about the "angle addition" rule or something, so what I have so far is:

(sin(x+dx)-sinx)/(dx)-->(sinxcosdx+sindxcosx-sinx)/(dx)-->(sinx-sinx+sindxcosx)/(dx)-->(sindxcosx)/(dx)-->(sin0cosx)/0=limit does not exist

but the limit should definitely exist at all times except when sinx-->0, which it isn't necessarily doing.

So, the problem I am assigned is:

"analytically simplify the following limit, which represents the definition of the derivative f'(a) for the function f(x)=sinx and x=a."

My teacher doesn't give the limit, and so I don't know where to start. The substitute (since the teacher wasn't there yesterday) said something about about the "angle addition" rule or something, so what I have so far is:

(sin(x+dx)-sinx)/(dx)-->(sinxcosdx+sindxcosx-sinx)/(dx)-->(sinx-sinx+sindxcosx)/(dx)-->(sindxcosx)/(dx)-->(sin0cosx)/0=limit does not exist

but the limit should definitely exist at all times except when sinx-->0, which it isn't necessarily doing.