Math CentralQuandaries & Queries


Question from Samantha, a student:

lim x-> 0 ( ( r*cos(wt +h) + r*cos(wt) )/ h )

Where r & w are constants.

I have r*lim ( (cos(wt)cos(h)-sin(wt)sin(h) + cos(wt)) / h)

r(w*lim cost)*(lim cosh/h) - r(w*lim sint)*(lim sinh/h) + rw(lim cost/h)

rw(1)*(?lim cosh/h) - rw(0)(1) + rw(1)*(lim 1/h)

Any idea?


I think you want the limit as h approaches zero not as x approaches zero.

I agree with you that

r × cos(wt +h) + r × cos(wt) )/ h = r × (cos(wt)cos(h)-sin(wt)sin(h) + cos(wt))

but your next step is not correct. cos(wt) ≠ w cos(t). What you need to do with

cos(wt)cos(h)-sin(wt)sin(h) + cos(wt)

is to rearrange it as

cos(wt)[cos(h) + 1] - sin(wt) sin(h)

Thus the limit becomes


Are you sure you have the original question written correctly?


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