Sunday, June 9, 2013

01:48:07

You will have 180 minutes to complete this exam. Answer all questions below. Feel free to use a calculator and refer to textbooks to help you complete the exam. You will need to receive a minimum score of 51/60 in order to pass, so please answer carefully and check your work. Please note: If you do not answer at least 51/60 questions correctly, you will not be able to retake an exam for this subject for 3 days. If you fail more than 1 exam for a given subject, you will not be considered for tutoring that subject. Good Luck!

Click here and choose the appropriate subject to view the Concept List. To ensure that the test loads properly and there are no formatting issues, please do not proceed unless you are using Internet Explorer 7 or greater.
Calculus
#1: *
#2: *
#3 Find the horizontal asymptote of the following function:: *
#4 Which of the following statements must be correct?: *
#5 Describe the limit of f(x) as x approaches 4.: *
Questions 6 - 7: Consider a function f(x), differentiable on [-1, 5]. Suppose f(1) = f(4) = 0 and f(3) = 6.

#6 Which of the following is not necessarily true? : *
#7 What is the average rate of change on [1, 3]?: *
#8 Which is an example of a function that is continuous at x = 5 but not differentiable at x = 5?: *
#9 What value of c will make f(x) continuous at x = 3?: *
#10 Find the derivative of g(x) = (x3 – 5)(x + 4).: *
Questions 11 - 13: Suppose f(x) and g(x) are differentiable functions on [-5, 5] and have values given by the following table:: *
: *
#13 Find (f o g) ’(-2), where o denotes usual functional composition.: *
#14: *
#15 If f(x) = sin2(e3x), find f ’ (x): *
#16 Find the derivative y’ of the equation x + y = xy.: *
#17 Which of the following functions satisfy f(ab) = f(a) + f(b) for all positive real values a and b?: *
#18 Which of the following are the domain and range, respectively, of f(x) = Arctan(x) where Arctan denotes the principal inverse tangent function?: *
Questions 19 - 21: Consider the following graph of the derivative f‘(x) of a three times differentiable function f(x), defined on the open interval (-3, 3) (thus f ’, f ’’, and f ’’’ all exist). Do not consider any behavior outside of this interval in answering.: *
#20 At what value(s) of x, if any, does f(x) have a local maximum?: *
#21 On which of the following intervals is f ’(x) concave up?: *
#22: *
#23: *
#24: *
#25: *
#26: *
For 27-28, consider the graphs y = 2x and y = 2x2 on [0, 1].

#27 Let S be the region enclosed by those graphs. What is the volume of the solid generated when S is revolved about the line y = 3? : *
#28 The area bounded by the two curves on [0, 1] is given by: *
#29: *
#30: *
#31 Find the maximum value of f(x) = 18x – 6x3 on [-2, 5].: *
Question 32 uses the following slope field for a particular differential equation.: *
For questions 33-34, assume f(x) is twice differentiable on [1, 7], f(1) = 0, f(7) = 6, f(3) = 4, f ’(3) = 0, and f ’’ (3) = -2.

#33 Which of the following must be true? : *
#34 Where does f(x) assume its absolute maximum on [1, 7]?: *
#35 Two people are 50 feet apart. One of them starts walking north at a rate so that the angle θ between the two people’s paths is changing at a constant rate of 0.01 radians per minutes. At what rate is the distance between the two people changing when the θ = 0.5 radians?: *
#36 Suppose the length of a diagonal of a square increases from 16 cm to 16.1 cm. What would the change in the area of the square be?: *
#37: *
#38: *
#39: *
#40 Suppose f(x) is twice differentiable on [0, 7]. If f(3) = 5, f ’(3) = 2, and f ’’(3) = -1, which of the following statements is/are correct?: *
#41 Let x = t5 - 4t3 and y = t2 be parametric equations. Find the first derivative for this set of parametric equations at t = 1.: *
#42 Let f(3) = 5, f(5) = 2, f ’ (3) = 4, and f ’(5) = 9. Let g(x) be the inverse of f(x) and assuming both f(x) and g(x) are differentiable for all real numbers. Find g’(5).: *
#43 Find the Maclaurin series expansion of f(x) = e2x.: *
#44 Let Sk = 3 - (k - 1) be a sequence starting at k = 1. To what value does the sequence Sk converge?: *
#45: *
#46 Which of the following series converge?: *
#47: *
#48: *
Questions 49 - 51: Define the two vectors a = <1, 3, -4> and b = <0, 5, 1>

#49 Find the dot product. : *
#50 Find the cross product.: *
#51 The angle x between vectors <-1, 1, 3> and <2, 0, -2> is given by solving which equation?: *
#52 Consider the function y = x2 + 4. Compute the left endpoint, right endpoint, and midpoint approximations to the area under the curve on the interval [0, 2] with four subdivisions. Which of the following statements is correct?: *
#53 Find the arc length of y = sin(√x) on [a, b] where a and b are positive.: *
Questions 54 - 56: A particle is moving with the velocity function v(t) = t2 – 14t + 48.

#54 At what point(s) does the particle have zero acceleration? : *
#55 Where is the particle moving backwards?: *
#56 Let s(t) represent the position of the particle at time t and suppose the initial position is 10. Find s(2) rounded to the nearest integer.: *
#57: *
#58 Which integral can be used to calculate the area enclosed by the smaller loop of the graph of the polar equation r = 1 + 2 sin θ?: *
#59 Which of the following is not necessarily true about a real-valued function f(x)?: *
#60 All of the following statements are always correct for functions f(x) and g(x) except:: *

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