1.曲线y=1/2x^2-2在点（1,-3/2)处切线的倾斜角为?2.已知f'(x0)=lim[f(x)-f(x0)]/(x-x0),f(3)=2,f'(3)=-2,则lim[2x-3f(x)]/(x-3)的值是?3.已知曲线y=x^2-1上两点A(2,3),B(2+△x,3+△y),当△x=1时,割线AB的斜率是?；当△x=0.1

Question

1.曲线y=1/2x^2-2在点（1,-3/2)处切线的倾斜角为?
2.已知f'(x0)=lim [f(x)-f(x0)]/(x-x0),f(3)=2,f'(3)=-2,则 lim[2x-3f(x)]/(x-3)的值是?
3.已知曲线y=x^2-1上两点A(2,3),B(2+△x,3+△y),当△x=1时,割线AB的斜率是?；当△x=0.1时,割线AB的斜率是?

Answer 1

1.dy/dx=x ===> tan p=1 ===> p=pi/4
2.[2x-3f(x)]/(x-3)
=[2x-3(f(x)-f(3))-3f(3)]/(x-3)
=[2x-3f(3)]/(x-3)-3[f(x)-f(3)]/(x-3)
=[2x-3*2]/(x-3)-3f'(3)
=2-3(-2)
=8
3.△x=1===>B(3,8)===>△y=5===>△y/△x=5