Question

Limit as x approaches 0 of x(1-cosx)/t-sinx.

Confused on how to get this answer.

Answer 1

what's the "t" doing there? Assuming it's suposed to be an "x" (or the denominator is not zero), we have

x(1-cosx) / x-sinx

taking derivatives top and bottom, we have

(xsinx - cosx + 1) / (1-cosx)
still 0/0

derivatives again gives

(2sinx + xcosx)/sinx
still 0/0

derivatives again gives

(3cosx - xsinx)/cosx
and that is just 3