Let f be a real valued differentiable function on ℝ (the set of all real numbers) such that f (1) = 1. If the Y–intercept of the tangent at any point P (x, y) on the curve y = f (x) is equal to the cube of the abscissa at P then the value of f (−3) is equal to
My Self Assessment
a) 9
Let f: [1, ∞) → [2, ∞) be a differentiable function such that f (1) = 2. If for all x ≥ 1 then the value of f (2) is
Let f be a real-valued function defined on the interval (-1, 1) such that f(x) = 2 + dt for all x ε (-1, 1) and let be the inverse of f. Then is equal to
a) 1
b)
c)
d)
If a polynomial of degree 3, then equals
a)
d) a constant
The order of the differential equation whose general solution is given by is
a) 5
b) 4
c) 3
d) 2
A solution of the differential equation is
a) y = 2
b) y = 2x
If is a solution of and then is equal to
c) 1
If then
If and then equals
d) 1
A spherical rain drop evaporates at a rate proportional to its surface area at any instant. The differential equation giving the rate of change of the radius vector of the rain drop is . . . . .
Solve the differential equation (12x + 5y – 9) dx + (5x + 2y – 1) dy = 0
b) = 2 [ln (x + 13) – ln (y – 33)] + c
c) = ln (x + 13) + ln (y – 33) + c
Solve the differential equation (secx tanx tany – ex) dx + secx sec2y dy = 0
a) secx tany = c
b) secx tany = ex + c
c) secx + ey = c
d) tany + ex = c
Solve the differential equation (x + y) (dx – dy) = dx + dy
a) y + ln (x + y) = c
b) x = ln (x + y) + c
d) y – x + ln (x + y) = c
Solve the differential equation ydx – xdy = 0
a) x = cy
b) xy = c
c) x = cy2
d) x2y = c
Solve the differential equation
Solve the differential equation ydx – xdy = xydx
Solve the differential equation tanx dy = coty dx
Solve the differential equation (2x + y) dy = (2y – x) dx
Solve
Solve (x + 2y) (dx – dy) = dx + dy
= 2 [ln (x + 13) – ln (y – 33)] + c = ln (x + 13) + ln (y – 33) + c
