OC userin Mathematics·18 May 20183. (18 pts) Show your work. Let f be a function defined by f(x) = x12 (a) Write the form of the limit and evaluate the limit. Do not use L'Hôpital's Rule. Show your work. 12 12 - 40=(0) - -= lim - 2 = * + 2) = Lima (68–1672 - FORM: (b) Find the natural) domain off. Write your answer in interval notation. (-0, -2) (-2, +00) (c) Let f-1 be an inverse of f. Find an expression for f-1(x), for x in the domain of f-1. = y(x + 2) = 12 yx + 2y = 12 = xy = 12 - 2y = 12 - 2y x= -- x= 12 - 2, and by switching x and y, we get y= 12 - 2 f(x) = 12 (d) Find the value or say "does not exist" (DNE). 1.84(f(n)) = 1 ii. f(p-10)) = DNE, because 0 is not in the domain of f-1
OC userin Mathematics·20 May 201815. (5 points) Given g'(x) below, which of the following statements is correct? O g(0.4) g(1.2) 0.4 0.8 1.2 O None of the above state ments can be determined with knowing more information. -2
OC userin Mathematics·18 May 20182. (10 marks) Compute the following limits, or explain why they do not exist. 2 - 4.0 (a) lim 2-122 - 3 - 4 (b) lim VX-3 2 -- 81 (c) lim f(x), where
OC userin Mathematics·17 May 20184. (a) Compute the 3rd degree Taylor polynomial of f(1) = e-31 at a = 0. Answer:
OC userin Mathematics·18 May 2018Problem 8. Let / 1 3 3 A= 0 1 2 (001) Find the (2, 3)-entry of the inverse of the matrix A. A) 3; B) – 3; C) 2; D) -2; E) 0; F) none of these.
OC userin Mathematics·18 May 20182. [5 marks] Using matrix B, answer the following: (a) The columns of B are: LI / LD. (circle the correct response) (b) The rank of B is: (c) What is the basis for the column-space of B? (d) Does basis{ColB} also form a basis for R? response) YES / NO (circle the correct
OC userin Mathematics·18 May 201810. Let A be the average value of f(x) = rex over the interval (1,2). Which of the following statements is true? (A) A
OC userin Mathematics·16 May 201810. Recall that the half-life of Carbon-14 (C-14) is 5730 years. (b) If you found today an old bone containing 70% of its original amount of C-14, how old would that bone be?
OC userin Mathematics·15 May 201812. [8 points) The demand equation for a product is p=0.0192 - 1.19 +30 and the supply equation is p=0.019? +8. Determine the consumers' surplus and producers' surplus when market equilibrium has been established.
OC userin Mathematics·17 May 2018Problem 5. (10 points) Steve sells cars at a local dealership. The number, X, of cars he sells on a given day is uncertain, but an estimate of the probability distribution for X is: Cars sold Probability 0.2 0.45 0.25 0.2 0.45 0.25 (b) Steve earns both a salary and a commission for selling cars so that his total earnings, Z, for the day are given by the following linear formula: 2-50 + 200X Find the mean of Z, which represents Steve's average daily earnings
OC userin Mathematics·16 May 20183 In 3 - 4 In 2 4 ln 3 - 3 In 2 3 In 3 - 6 In 2 4 In 3 - 6 In 2 € 4 In 3 - 8 In 2
OC userin Mathematics·16 May 2018PROBLEM 14: At a student technology cluster on campus, 80% of the computers are PC's, and the other 20% are Macs. It is also the case that 70% of the PC's do not work correctly. and 5% of the Mac's do not work correctly. If a student randomly chooses a computer, and the computer does not work correctly, what is the probability that it is a PC ? A) 24/43 B) 0.57 C) 56/57 D) 0.56 E) 0.92 N) none of the above
OC userin Mathematics·17 May 20181 10. Letf(x) = x² +3 --- 1. Its derivative satisfies 1 2.03 + x2 +1 (x + 1)(2.2 - 2+1) f'(x) = 2x +1+ = 22 (a) Evaluate lim f(c) and lim f(). 100- 20+
OC userin Mathematics·15 May 2018A company has taxable income of $50,000. The federal tax is 10% of that portion that is left after the provincial tax has been paid. The provincial tax is 15% of that portion that is left after the federal tax has been paid. If x denotes the federal tax and y denotes the provincial tax, write a system of equations and solve it. What's the total of the taxes paid? Round your answer to the nearest dollar.