Find all real valued continuously differentiable functions f on the real line such that for all x,
My Self Assessment
a)
Solve
Solve , given that y = 1 when x = 1
The normal to a curve at P(x, y) meets the x – axis at G. If the distance of G from the origin is twice the abscissa at P, then the curve is
a) Ellipse
b) Parabola
c) Circle
d) Hyperbola
A point on the parabola y2 = 18x at which ordinate increases at twice the rate of the abscissa, is
a) (2, 4)
b) (2, −4)
c)
d)
A function y = f(x) has a second order derivative through (2, 1) and at that point tangent to the graph is y = 3x – 5 then the function is
a) (x − 1)2
b) (x − 1)3
c) (x + 1)3
d) (x + 1)2
If then f(x) =
b)
Solve ysin2xdx – (1 + y2 + cos2x) dy = 0
Solve y (x2y + ex) dx – ex dy = 0
Solve y (axy + ex) dx – ex dy = 0
Solve 2xydy = (x2 + y2 + 1) dx
Solve xdy – ydx + 2x3dx = 0
Solve xdy – y dx = xy2dx
Solve ydx – xdy + (1 + x2) dx + x2sinydy = 0
Solve y (1 + x) dx + x (1 – y) dy = 0
Solve (y – xy2) dx – (x + x2y) dy = 0
Solve (1 + xy) x dy + (1 – xy) y dx = 0
