OC userin Mathematics·25 Dec 20173. (10 marks) A paper cup has the shape depicted below. All of its horizontal cross sections are circles; the radius of the cup's bottom is 3cm and the radius of its top is 6cm. The cup is full of water, which has a density of 1000kg/m". The water is drunk through a vertical straw that extends 10cm above the top of the cup and reaches the bottom of the cup. Express as an explicit definite integral the work performed in drinking all the water. Do not evaluate this integral. For the acceleration due to gravity use the value 9.8m/sec. 20 cm
OC userin Mathematics·25 Dec 2017The proportion of students who own a cell phone on college campuses across the country has increased tremendously over the past few years. It is estimated that approximately 90% of students now own a cell phone. Fifteen students are to be selected at random from a large university. Assume that the proportion of students who own a cell phone at this university is the same as nationwide. Let X = the number of students in the sample of 15 who own a cell phone. 17. What is the probability that all students in a simple random sample of 15 students own a cell phone? A) 0 B) 0.1 C) 0.206 D) 0.9
OC userin Mathematics·23 Dec 20174. (24 pts) if x < 0 and x # - 2 Let g(x) = x + 2 I e-*+C if x 20. (I) Evaluate the limit. Show your work. (Note: possible answers may include - or .) (a) (4 pts) lim g(x) = ; (b) (4 pts) lim g(x) = 9 (X) = *+-2+ (c) (2 pts) lim g(x) (a) (2 pts) lim x++00 g(x) = X -00 a m u i c Orc = Хva x+ ) C+C =0tr X (II) (2 pts) Find (the equations of) all vertical asymptotes. X=-2 (III) (4 pts) Find (the equations of) all horizontal asymptotes. 451 4= C (IV) (6 pts) Determine the value of the constant c for which lim g(x) exists. x+0
OC userin Mathematics·25 Dec 20176. Let f(x) = on [1/2,5/2). Let M be the absolute maximum value of f on [1/2,5/2] and let m be the absolute minimum value of f on 1/2,5/2] . Then M -m=
OC userin Mathematics·23 Dec 20173 Consider the function f (a) = * + 1 Its first and second derivatives are given by f'(x) = - by fee_*2 +1 (2x2 - 1) and and I" (2) - 20 (x2 + 3) (221) D. Find the intervals where the function is concave up, concave down and the (2, y) coordinates of the inflection point(s). Write DNE if they don't exist.
OC userin Mathematics·22 Dec 20174. [10 marks) Let T:R' RP be the linear transformation defined by I = 2:01 - 403 22-23 + 3.74 Il +.12 - 3.13 +2.04 ) (a) Find the image of the vector, ID=|| i by applying the given transform, T. (b) Find the standard matrix of T. (c) Find the image of rd (above) by matrix multiplication of the standard matrix of T and rp. Compare your answer to (a). (d) Find the vector from the domain, cd, which gives the image cr=| 1 in the range of T.
OC userin Mathematics·23 Dec 20171. Find the point(s) on the curve 12 + xy + y2 = 9 for which the slope of the tangent is equal to 1. [9 points)
OC userin Mathematics·22 Dec 201722+6 1. Find all vertical asymptote(s) of f(0) = -2 23 - 4.12 - 12. A. r = 0 f(x=(x-3) *( x-6) D. x = -2 E. x = 3
OC userin Mathematics·24 Dec 2017(i) Find an approximation to In(1.25) by using the linear approximation to f(2)= In(x) at a= 1. Answer:
OC userin Mathematics·23 Dec 20177. NOTE: This is a hard question and will be marked very strictly. Very little or no credit will be given unless you can get the final answer and your solution is completely correct. b dx Let a and b be constants such that a
aquamarinefox966Lv1in Mathematics·22 Dec 20174. A linear system is represented by the following augmented coefficient matrix 1-1 -32 0 2 21-11 0 1 11-1 How many solutions will this linear system have? A) no solutions B)exactly one solution C)exactly two solutions D)infinitely many E) none of these