Which one of the following is the differential equation that represents the family of curves
where c is an arbitrary constant ?
Which one of the following is the second degree polynomial function f(x) where f(0) = 5, f( - 1) = 10 and f(1) = 6 ?
5x2 – 2x + 5
3x2 – 2x – 5
3x2 – 2x + 5
3x2 – 10x + 5
Consider the following statements :
1) The function f(x) = ln(x) increases in the interval (0, ∞).
2) The function f(x) = tan(x) increases in the interval
Which of the above statements is/are correct ?
1 only
2 only
Both 1 and 2
Neither 1 nor 2
The function u(x, y) = c which satisfies the differential equation x(dx – dy) + y(dy – dx) = 0, is
x2 + y2 = xy + c
x2 + y2 = 2xy + c
x2 - y2 = xy + c
x2 - y2 = 2xy + c
The solution of the differential equation is
y = tan(x) + c
y = tan(x + c)
tan-1(y + c) = x
tan-1(y + x) = 2x