MATH 151, FALL 2017 COMMON EXAM 2, VERSION B. LAST NAME (print) : FIRST NAME (print): INSTRUCTOR : SECTION NUMBER: DIRECTIONS THE AGGIE HONOR CODE

Size: px

Start display at page:

Download "MATH 151, FALL 2017 COMMON EXAM 2, VERSION B. LAST NAME (print) : FIRST NAME (print): INSTRUCTOR : SECTION NUMBER: DIRECTIONS THE AGGIE HONOR CODE"

Gervase Wilkinson
6 years ago
Views:

1 MATH 5, FALL 7 COMMON EXAM, VERSION B LAST NAME (print) : FIRST NAME (print): INSTRUCTOR : SECTION NUMBER: DIRECTIONS. The use of a calculator, laptop, or computer is prohibited.. TURN OFF cell phones and put them away. If a cell phone is seen during the exam, your exam will be collected and you will receive a zero. 3. In Part (Problems 6), mark your choice on your ScanTron using a No. pencil. The scantrons will not be returned. Therefore, for your own records, circle your choices on your exam!. In Part (Problems 7 ), present your solutions in the space provided. Show all your work neatly and concisely and clearly indicate your final answer. You will be graded not merely on the final answer, but also on the quality and correctness of the work leading up to it. 5. Be sure to write your name, section number, and version letter of the exam on the ScanTron form. THE AGGIE HONOR CODE An Aggie does not lie, cheat, or steal, or tolerate those who do. Signature:

2 Part : Multiple Choice ( points each). A bacteria culture doubles every 3 hours. Assuming the culture grows at a rate proportional to itself, how many hours will it take the culture to be three times its initial size? (a) 3ln3 9 (b) ln 3ln ln3 (d) 9 (e) 3ln3 ln. Find an equation of the tangent line to the graph of x = t t, y = (t 6) 3 at the point where t =. (a) y 8 = (x 8) (b) y 8 = 8 (x 8) y 8 = (x 8) (d) y 8 = (x ) (e) y 8 = 8(x 8) 3. If g(x) = f ( x ) 3x find g () given that f () = 3 and f () =. (a) 3 6 (b) (d) 3 (e) 6. Use the linear approximation to the function f (x) = 3 x at x = 8 to approximate the value of (a) 39/ (b) / 9/ (d) 3/ (e) 5/

3 5. Find the slope of the tangent line to the graph of f (x) = x ln ( x 3 + ) at the point where x =. (a) ln + 3 (b) ln + 3 (d) 3 (e) ln + 6. The tangent line (linear) approximation for f (x) at x = is y = 5x +. If g(x) = f (x), find the tangent line (linear) approximation for g(x) at x =. (a) y = + (x ) (b) y = (x ) y = (x ) (d) y = + 5 (x ) (e) y = + 9 (x ) 7. Which of the statements is true about f (x)? 3x +, x < f (x) = x 3 + 8, x 3 x + 5, x > 3 (a) f is not continuous at x = or x = 3. (b) f is continuous but not differentiable at both x = and x = 3. f is differentiable at both x = and x = 3. (d) f is continuous but not differentiable at x = ; f is differentiable at x = 3. (e) f is differentiable at x = ; f is continuous but not differentiable at x = Find the slope of the tangent line to the curve x + y = at the point (,). 8 (a) (b) 8 (d) (e) 3

4 9. For what values of x on the interval [, π) does the graph of f (x) = sinx + x have a horizontal tangent? (a) x = 3 π, 3 π (b) x = 3 π, 3 π x = 5 6 π, 7 6 π (d) x = 3 π, 5 3 π (e) x = 6π, 6 π. Find the 3rd derivative of f (x) = cos3x. (a) 3 3 cos3x (b) 3 3 sin3x 3 3 cos3x (d) 3 3 sin3x (e) None of these. The radius of a sphere was measured to be 5cm with a maximum error in measurement of.cm. Use differentials to estimate the maximum error possible in the calculated volume of the sphere. (The volume of a sphere is V = 3 πr3.) (a) π (b) π 5 π (d) 5 3 π (e) 5 π. Which of the following is a tangent vector to the curve r(t) = [ t 3t, t 3 ] at the point (, )? (a) [,] (b) [5,] [ 5,3] (d) [5,8] (e) [,3]

5 3. Find f (x) for f (x) = e /x. ( ) (a) x e /x ( (b) x 3 ) x e /x ( x ) 5 e /x ( (d) x 3 + ) x e /x ( (e) x 3 ) x 3 e /x. Find f (x) for f (x) = ln ( ) x 6 + sec. [HINT: First use properties of logarithms.] x (a) (b) (d) (e) x 5 secxtanx 3x 5 x 6 + tanx x 5 secxtanx 3x 5 x 6 + tanx secx 3x 5 x 6 + tanx 5. For what value(s) of t does the graph of x = t 3 3t, y = t 3 + 6t have a vertical tangent? (a) t =, 3, 3 (b) t =, 3 t =, (d) t =, (e) There are no vertical tangents. 6. The position function of an object is given by f (t) = t 6t + 5. Find the total distance traveled by the object from t = to t =. (a) 8 (b) 3 (d) 9 (e) 5 5

6 Part : Work Out DIRECTIONS: Present your solutions in the space provided. Show all your work neatly and concisely and box your final answer. You will be graded not merely on the final answer, but also on the quality and correctness of work leading up to it. 7. ( points) A trough with isosceles triangles at its ends is being filled with water a rate of m 3 /s. The trough is m long. Its height is 5m and the width across the top of the tank is m. Find the rate at which the height of the water in the tank is rising when the height of the water is m Trough End 8. ( points) Find the derivatives of the following functions. (a) f (x) = cot3 ( x ) x + x (b) g(x) = (5x + ) arcsinx 6

7 9. (8 points) Find dy dx for the equation esinx y 3 x = sec(y).. (6 points) Find the values of a and b so that the line y = x + b is tangent to the graph of f (x) = ax 3 x at the point where x =. FOR INSTRUCTOR USE ONLY! Question Points Awarded Points M/C Grand TOTAL 7

MATH 151, SPRING 2018

MATH 151, SPRING 2018 COMMON EXAM II - VERSIONBKEY LAST NAME(print): FIRST NAME(print): INSTRUCTOR: SECTION NUMBER: DIRECTIONS: 1. The use of a calculator, laptop or computer is prohibited. 2. TURN OFF