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| Math Central | Quandaries & Queries |
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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? |
Samantha,
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?
Harley
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