OC userin StatisticsΒ·19 Mar 20182. [5 marks) For the function f(2) - compute the limit f(x+h)-f(x) lim h0 h Show all of your work. Only partial credit will be given for the answer if no work is shown.
OC userin StatisticsΒ·17 Mar 20187. The minimum value taken by the function f(x) = 3 sin(I) β 2 cos(x) on [0, 1] is (a) β2, (b) -4, (c) 5, (d) β12, (e) β10.
OC userin StatisticsΒ·17 Mar 2018(b) Find the minimum and maximum values achieved by q(X) on the unit circle xα» + xΕΎ= 1.
OC userin StatisticsΒ·15 Mar 201816. Let T:R2 R2 be a non-zero linear transformation with standard matrix A, and let det(A) = 0. Which of the following statements is true? A) The parallelogram formed by T . and T0 ) has area 1. B) There is a linear transformation S: R2 + R2 such that SoT is the identity transformation. C) dim (span {7 ( 6 ) 7( ')}) β 1. D) For every vector b E R2, there is a vector u β¬ R2 such that T(u) = b.
OC userin StatisticsΒ·12 Mar 20184. Suppose that A and B are 4 x 4 matrices and that det(A) = det(B) = det(-ABAT(-3B2)(-A)-1) is . Then
OC userin StatisticsΒ·4 Mar 20187. (10pts) (a) Find the solution of the system 3-y+32 = -1 x + 3y - 2=3 2 + y + 5z = 1 that is closest to the point P(1,-1,0) in R3.
OC userin StatisticsΒ·5 Mar 2018(5) Using the definition of the derivative show that the function f(T) = 1-12 4 2 if i<1 if I > 1. is not differentiable at x = 1.
OC userin StatisticsΒ·4 Mar 2018(8) A function f(x) is defined for all positive real numbers and satisfies the equation f(x3) = ?? for every r > 0. Find f'(8).
OC userin StatisticsΒ·28 Feb 201814. Consider f(x) = x3 - 8x+3 on the interval [ -3,3]. The intermediate value theorem, applied to this interval, guarantees the existence of a number xo between β 3 and 3 such that f(x0) equals (a) -5 (b) - 4 (c) 10 (d) 2 (e) 11
OC userin StatisticsΒ·24 Feb 20189. The rank of 3 2 1 4 7 0 90 2 5 6 0 | 12 7 16 4 ) Is (A) 1, (B) 2, (C)3, (D) 4.
OC userin StatisticsΒ·23 Feb 20184. Consider the function f(x) = 4x3 - 22 - 1 (c) [2 marks] Using the intermediate value theorem, prove that f(x) must have a root between 0 and 1.
OC userin StatisticsΒ·24 Feb 20186. Find lim 2-0 1 - cos(x) 73 (a) 1/2, (b) 1, (c) 2, . (d) 0, (e) does not exist.
OC userin StatisticsΒ·22 Feb 20183. If Arab 3. A ed has determinant -3, B = has determinant -1, and C=1 c a + 2ab d +25 ), then the determinant of-4CB-' is (a) -60. (c) 80. (d)-80. (e) None of the above.