2.lim {(2x^2+3x+4)^1/2-ax-b}=0 (x->無限大) find a and b
3.suppose that f satisfies the equation. f(x+y)=f(x)+f(y)+x^2 y+x y^2 for all real numbers
x and y. suppose further that lim f(x)/x=1(x->0). find f'(x)
4.f(x)=xsin(1/x) if x≠0, f(x)=0 if x=0. find f'(0).
5.find the derivative dy/dx, y=(sinx)^1/2
6.find the derivative dy/dx. y=cos^2{tan(sin2x)^1/3}
7.G(x) satisfies the differential equation xy"+y'+xy=0 for all values of x and G(0)=1.
find G"(0)
8.show that the sum of the x- and y- intercepts of any tangent line to the
curve x^1/2+y^1/2=m^1/2 is equal to m.
9.find the equation of the tangent lone at the indicated point. y=-cos(xy^2)+3x^2=4;(1,0)
10.2x^3-3y^2=4 find the second derivative d^2 y/d x^2 at(2,2)
11.find the linear approximation to f(x)=1+sin(2x) at x=π/2
更新1:
9.find the equation of the tangent "line" at the indicated point. "y+cos(xy^2)+3x^2=4" ;(1,0) " "為訂正部分.謝謝
