Find the derivative of the following functions with respect to x: (2+2)
(i) (x⁻¹ᐟ² - x¹ᐟ²)/(x⁻¹ᐟ² + x¹ᐟ²)
(ii) 3x/√(5+2x²)
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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.
Find A⁻¹, where
Solve the following system of equations using Cramer's rule.
x + y - z = 6
3x - 2y + z = -5
x + 3y - 2z = 14
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.
∫(2eˣ - 3√x)dx
(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.
∫((1+ln x)³)/x dx