2. [18 Marks] For the given sketch of y = +2, y = x +2. 1) Find the intersection points A, B and C. (Do not Estimate!) 4 [7 Marks) B 15FMAT127 Assignment 2 Page 2 of 3 [11 Marks) ii) Determine the shaded area enclosed between the given two curves x3 y = +2, y = x +2 15FMAT127 Assignment 2 Page 3 of 3
1. .] For the following function f(x)= x* – 2x - 5 Determine the Inflection Points ONLY 2. For the given sketch of y i) Find the intersection points A, B and C. (Do not Estimate!) ***2, y =x +2; ii) Determine the shaded area enclosed between the given two curves y =*+2, y=x+2
Problem 5 20 marks total 0 < y < x2 < Consider two rvs X and Y with joint pdf f(x,y) = k-y, Sketch the region in two dimensions whereAx.y is positive. Then find the constant k and sketch /fx.y) in three dimensions. I4 marksl (a) Find and sketch the marginal pdf/(x), the conditional pdf ffr11/2), and the conditional cdf F11/2) (b) 4 marks] Find P(XcYlY> 1/2), E(XIY=1/2) and E(XlY>1/ 2). /4 marks/ (c) (d) What is the correlation between...
Use the steps below to sketch the graph y = x^2 - 7x - 18. Required points are the x intercepts and the max and mix of the graph 1. Determine the domain of f. 2. Find the x- and y-intercepts of f.† 3. Determine the behavior of f for large absolute values of x. 4. Find all horizontal and vertical asymptotes of the graph of f. 5. Determine the intervals where f is increasing and where f is decreasing....
6. [5 marks] Find and classify all stationary points of f(x,y) xy+2xy 7. [6 marks] Sketch the region of integration and evaluate the iterated integral 2 r2 JC 10 (y+xy-2) dxdy. 6. [5 marks] Find and classify all stationary points of f(x,y) xy+2xy 7. [6 marks] Sketch the region of integration and evaluate the iterated integral 2 r2 JC 10 (y+xy-2) dxdy.
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent planes to the two surfaces at P(2,0,-8) are perpendicular. whether the lines parallel, 2-z & 12 Marks] 4x2 +9y2-24. (B) Find the points on Si at which the tangent plane is parallel to the plane x+y+32-5 3 Marks] Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or...
1. .) For the following function f(x)= x4 – 2x - 5 Determine the Inflection Points ONLY 2.. For the given sketch of y = :) Find the intersection points A, B and C. (Do not Estimate!) +2, y=x+2= ii) Determine the shaded area enclosed between the given two curves -*+2, y =x +2
Question 20 The solution to the linear inequality − 10 x + 2 y > − 4 will be the half-plane lying a) on and below the solid line − 10 x + 2 y = − 4. b) below the solid line − 10 x − 2 y = − 4. c) above the dashed line − 10 x + 2 y = − 4. d) on and above the solid line − 10 x + 2 y = − 4. e) below...
QUESTION 5 Consider the function f(x,y) – In19 – x? –y?) X+2 a) Find and sketch the domain of the given function. b) Show that the function is continuous at (2-2). (5 marks) (3 marks)
QUESTION 1 (15 MARKS) a) Given the line Lj: I = 2 - 2t, y = 5 + 2t, z=t-1 and 1 1 - 2 L2 : =y-3 = 2 4 i. Check whether the lines Lị and L2 parallel, intersect or skewed? (5 marks) ii. Find the shortest distance from the point (1, 2, -1) to the line Li- (3 marks) b) Given two planes 71 : 20 - 4y +z = 5 and T2 : 7x + y...