OC userin Statistics·16 Jan 201812. Given linearly independent vectors v and w, which one of the statements below is always correct when u=(w.w)v - (v.w)w A) w is orthogonal to v. B) u is orthogonal to v. C) u is a unit vector. D) u is orthogonal to w. E) u is the cross product of v and w.
OC userin Statistics·14 Jan 20181. 2.0 +1 Consider the function f(0) = 1 - 6 (a) [2 marks) Locate all vertical asymptotes for f(x)
OC userin Statistics·11 Jan 20183. Suppose that 2 and -5 are the only eigenvalues of the matrix A. Which of the following statements is true? A) 21 - A is invertible, and there is a nontrivial solution to Av = -5v. B) 21 - A is not invertible, and there is a nontrivial solution to Av = -5v. C) det(21 + A) = det(51 – A) = 0. D) det(21 + A) = 0, and there is a nontrivial solution to (51 – A)v = 0.
OC userin Statistics·13 Jan 2018sinh 2 (b) If , then the value of - ) when x = 0 is CS x+1, then the ANSWER ONLY
OC userin Statistics·8 Jan 20182. Let f(x) = x® In(x). Then f"(1) is (a) 7, (b) 5, (c) 9, (d) 3, (e) 2.
OC userin Statistics·6 Jan 2018Version 1 MATH 133 Final Exam - April 18, 2008 II.2 (15 points) Consider the matrix M = [1 1 | 1 2 1 2 3 5 | 1 3 4 5 5 14 6 -3 71 -5 8 -6 11 -13 23 -7 9 . (a) Find the reduced echelon form of M, showing your work. (You should find that M has rank 3.)
OC userin Statistics·3 Jan 20183. If det au 012 013 221 222 223 231 232 233) (A) 6 (B) (3a11 +231 3012 + 232 3013 + 233 = 4, then det 221 +211 222 +212 223 +013 has the value 231 + 2011 232 + 2a12 033 + 2013 - 6 (C) – 12 (D) 4 (E) None of the above.
OC userin Statistics·3 Jan 201814. The function defined by (sin(81) if x < 0, f(x) = { 2x la cos(5:) if x > 0. is continuous if and only if a is (a) 5, (b) 8, (c)4, (d) -1, (e) 0.
OC userin Statistics·1 Jan 2018(5) A function f(r) is defined for all positive real numbers and satisfies the equation $() = 23 for every 1 > 0. Find f'(4). Answer:
OC userin Statistics·2 Jan 20182. (10 marks) ex-y = xy. Determine the (a) Consider the curve C implicitly defined by the equation equation of the tangent line to Cat (1,1). (b) Compute the derivative of y = (sin x)sin .