OC userin Statistics·12 Oct 20186. Consider the following system of equations, depending on the parameter k. 21 +(k+1):22 +4x3 = 3 +(k+ 3x3 = 21 +222 +3x3 = . Which of the following is true? A) The system has a unique solution for every value of k. B) The system has no solution for any value of k. (C) The solution is unique if k = -1 and k + 2. There are no solutions if k = 2 or if k = -1. D) The solution is unique if k #1 and k #2. There are no solutions if k = 2 and infinitely many if k=-1. E) None of the above.
OC userin Statistics·12 Oct 2018(8) A function is defined as follows Slx - 4 + ax 1x2 - 2ar +4 if r < 2 if > 2. Find the value of a such that f(n) is continuous at := a.
OC userin Statistics·5 Oct 20188. the 2014th derivative of cosh x is (a) sinh x (b) cosh x c) tanh x (d) - coshx (e) - sinh x
OC userin Statistics·5 Oct 20183. Suppose that P and Q are 4 x 4 matrices, that R = adj(P2) and that det P = -2, det Q = 3. Then the determinant of -3R? PQ-4 is A)48 B)-128 C) -18 D)128 E)None of the above
OC userin Statistics·3 Oct 20183. Consider the function f(x) = 12 - VX| (c) [3 marks] Using your answer in part (b), show that f(x) is continuous on its domain. Justify your answer.
OC userin Statistics·3 Oct 20181. SHOW ALL YOUR WORK! (a) 4 MARKS] Let gr) = 1 + sinh 20. Showing all your work, find a linearization of g at a=0.
OC userin Statistics·3 Oct 20182. The system of equations 3.0 - 2z=0 3x + y - 4z=0 2x+y-2=3 (a) Has a unique solution, because the determinant of the coefficient matrix is zero. (b) Has a unique solution, because the determinant of the coefficient matrix is nonzero. (c) Has infinitely many solutions, because the determinant of the coeffi- cient matrix is nonzero. (d) Has infinitely many solutions, because the determinant of the coeffi- cient matrix is zero. (e) None of the above
OC userin Statistics·2 Oct 201813 2 4. The rank of 1 (3 1 3 1 1 2 -1 . -1 0 2 3 3 -1/ (A) 1 (B) 2 (C) 3 (1) 4 (E) None of the above
OC userin Statistics·2 Oct 2018(C) [3 MARKS] Use a linear approximation to y' to estimate the slope of the tangent line to the curve with equation arctan when x = 0.95.
OC userin Statistics·28 Sep 2018(7) A microbial population doubles in size every four days. How many days does it take to triple in size? (Your answer will be in terms of logarithms!) Answer:
OC userin Statistics·27 Sep 2018(d) (3 MARKS] Showing all your work, determine the concavity of the graph of f and find all inflection points.
OC userin Statistics·28 Sep 2018/ 2 1 1 2.3 (10 points) Given the matrix A= | 1 2 1 11 1 2 Find a diagonal matrix D and an orthogonal matrix P such that PT AP = D.