Practice 10 questions on MATH1722 - Mathematics Foundations: Specialist at The University of Western Australia. Free AI-generated quiz on uNotes — track your score, retake anytime.
Given that the cubic polynomial P(x) = x^3 + 4x^2 + 4x + 3 has a factor (x + 3), find the solution to the inequality x^3 + 4x^2 + 4x + 3 >= 0 for all real x.
2Determine the domain of the function y = 1/(x^2) + ln(x).
3A rectangle has one vertex at (0,0) and the opposite vertex (x,y) on the line 3x + 2y = 100 in the first quadrant. Calculate the maximum possible area of this rectangle.
4Water flows into a spherical container of radius 1m at a rate of 0.3 m^3/s. Using the volume formula V = pi*h^2*(1 - h/3), calculate the rate (in m/s) at which the water level is rising when the height h = 0.6m. Round your answer to four decimal places.
5Calculate the volume of the solid formed by rotating the region bounded by y = sqrt(cos(2x)cos(3x)) and the x-axis about the x-axis for the interval x in [0, pi/6].
6For the vectors u = (3, 4) and v = (2, -1), calculate the dot product u . v.
7Find the inverse of the coefficient matrix A = [[1, 1], [2, 3]] as determined from the system x + y = 9 and 2x + 3y = 4.
8Convert the complex number 1 + i to its polar form r(cos(theta) + i*sin(theta)) using the principal argument.
9In the proof by mathematical induction for the sum of squares of odd numbers, 1^2 + 3^2 + ... + (2n-1)^2 = (4n^3 - n)/3, what is the value of both sides for the base case n = 1?
10Using implicit differentiation, find the expression for dy/dx for the equation x^3 - sin(y) + x/y = 3.
