∫((1+ln x)³)/x dx
To evaluate the integral (\int \frac{(1+\ln x)^3}{x} , dx), we can use the substitution method. Let (u = 1 + \ln x). Then, (du = _______ _______ ___ ________ _______ _________ __________ __________.
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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.
Find the asymptotes of the following functions:
(i) (3x-4)/(2x+6)
(ii) (x²-2x-8)/(x-1)
(a) If A = 
then show that
(i) 1/2 (A + A') is symmetric, and
(ii) 1/2 (A - A') is skew symmetric.
(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}
(b) If A = {1, 2, 3}, B = {2, 3, 4, 5}, and C = {1}, determine A ∪ B ∪ C and also verify
A ∪ B ∪ C = (A ∪ B) ∪ C = A ∪ (B ∪ C)
∫(2eˣ - 3√x)dx
(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
∫₁³ x²eˣ³ dx