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.
For the first differential equation, ((1/y^2)(dy/dt) = 1 - e^{-3t}), multiply both sides by (y^2) to get (\frac{dy}{dt} = y^2 (1 - e^{-3t})). This is separable: (\frac{dy}{y^2} = (1 - e^{-3t}) dt). Integrating ________ _______ ____ ______ _______.
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∫((1+ln x)³)/x dx
Find the derivative of the following functions with respect to x: (2+2)
(i) (x⁻¹ᐟ² - x¹ᐟ²)/(x⁻¹ᐟ² + x¹ᐟ²)
(ii) 3x/√(5+2x²)
(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}
1.50 mol of PCl₅(g) is decomposes at room temperature to form PCl₃(g) and Cl₂(g). Determine their concentration at equilibrium, when K_c = 1.80.
Verify that the following matrix A is orthogonal
∫₁³ x²eˣ³ dx
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.