In an iron determination from the same amount of sample, the five replicate results were obtained: 20.1, 19.6, 20.0 and 19.9 and 20.4 mg iron.
Calculate the standard deviation, variance, standard deviation of mean, coefficient of variation and relative standard deviation in ppm of the given data.
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(a) Which of the following sets are finite, and which are infinite?
(i) The set of points on the circumference of a circle.
(ii) ]0, 1[
(iii) [-1, 1]
(iv) {1, 2, ..., 100}
Find the equation of tangent and normal to the curve f(x) = x³ - 3x² + 6x - 1 at x = 2.
Solve the following system of equations using Cramer's rule.
x + y - z = 6
3x - 2y + z = -5
x + 3y - 2z = 14
(dy/dx)³ = √(1+(dy/dx)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.
(a) Find eigenvectors for the matrix
(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