Question

f(x)=sinx,求{f(1+h)-f(1)}/h 结果{2sin h/2 cos 2+h/2}/h是如何求出来的

Answer 1

f(1+h)=sin(1+h),f(1)=sin1

[f(1+h)-f(1)]/h

=[sin(1+h)-sin1]/h

=2cos{[(1+h)+1]/2}*sin{[(1+h)-1]/2}

=2cos(1+h/2)*sin(h/2)

和差化积公式sina-sinb=2*cos{(a+b)/2}*sin{(a-b)/2}