Define Binomial, Poisson and Normal distribution with appropriate equation and name their terms.
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(a) Evaluate the following limit.
(b) If the law of motion of a particle is given as: s = -t³ + 3t² + 25, then (2+1)
i) find its velocity and acceleration.
ii) find the distance covered by the particle in time t = 5 units
(a) Two coins are tossed simultaneously then find probability of getting at least one head.
(a) Find the differential equation whose solution is given by
y = eˣ(A cos x + B sin x)
where, A and B are arbitrary constants.
Find A⁻¹, where
Define Binomial, Poisson and Normal distribution with appropriate equation and name their terms.
Find the equation of tangent and normal to the curve f(x) = x³ - 3x² + 6x - 1 at x = 2.
Solve the following differential equation:
(1/y²) (dy/dt) = 1 - e⁻³ᵗ
(c) Show that the equation
(y - 2x³)dx = x(1 - xy)dy
becomes exact on multiplication by x⁻² and solve it.