Question

11. Let f(1) = cos 1. Use the definition of the derivative to prove that f'(:1) = -sin . Solution: We have · f'(:1) = lim cos(2+h) - cos(2) +0 cos(1) cos(h) - sin() sin(h) - cos(1) = lim h0 sin / – Jin contar) (cos(1) = -1) = sin(e) (sinm) h0 sin(h) cos(h) - = lim cos(2) h cos(h) - 1 = cos(x) lim h- oh = cos(x)0 - sin(x)(1) = - sin h c) lim 0 / h