Department of Mathematical SciencesInstructor: Markus SchmidmeierCalculus IIAugust 26, 2016 Name:

Quiz 1

1. Consider an object moving long a line with velocity

v(t) = 6− 2t during the time interval [0, 4].

The initial position is s(0) = 0.

(a) Graph the velocity function on the given interval and determinewhen the object is moving in the positive direction and when itis moving in the negative direction.

(b) Determine the position function and graph the position functionon the given interval.

(c) Determine the displacement and the distance traveled over thegiven interval.

P.T.O.

2 Calculus II, Quiz 1, August 26, 2016

2. Consider the functions

f(x) = 3− x, g(x) = x2 + 1.

(a) Sketch the graphs of the line and the parabola.(b) Find the two intersection points.(c) Find the area between the two graphs.(d) Verify the result in (c) by making a (possibly rough) estimate.

Department of Mathematical SciencesInstructor: Markus SchmidmeierCalculus IISeptember 2, 2016 Name:

Quiz 2

1. (a) Make a sketch of the region R bounded by

y =√

sin(x), y = sin(x), x = 0, x = π.

(b) Find the volume of the solid generated when R is rotated aboutthe x-axis.

P.T.O.

2 Calculus II, Quiz 2, September 2, 2016

2. Consider the region R given by the triangle with vertices

(0, 0), (0, 2), (1, 2).

(a) Make a sketch of the region R and of the solid S obtained byrotating R about the y-axis.

(b) Find the volume of S. Which method are you using?

Department of Mathematical SciencesInstructor: Markus SchmidmeierCalculus IISeptember 9, 2016 Name:

Quiz 3

1. (a) Make a sketch of the region R in the first quadrant bounded by

y = x2, y = 1, x = 0.

(b) Find the volume of the solid generated when R is revolved aboutthe line y = −2. Which method are you using?(c) Find the volume of the solid generated when R is revolved aboutthe line x = 1. Which method are you using?

P.T.O.

6 Calculus II, Quiz 3, September 9, 2016

2. Make a sketch of the graph of the function given by

y = x3/2 on [0, 1]

and find the arc length on the given interval.

Department of Mathematical SciencesInstructor: Markus SchmidmeierCalculus IISeptember 16, 2016 Name:

Quiz 4

1. (a) Find the area of the surface generated when the upper part ofthe circle x2 + y2 = 400 on the interval [0, 10] is rotated about thex-axis.

(b) A 1.5 mm layer of paint is applied to one side of the surface in1.(a). Find the approximate volume of paint needed. Assume that xand y are measured in meters.

P.T.O.

6 Calculus II, Quiz 4, September 16, 2016

2. Suppose a force of 60N is required to stretch and hold a spring 0.5mfrom its equilibrium position.

(a) Assuming the spring obeys Hooke’s law, find the spring constant k.

(b) How much work is required to compress the spring 0.25 m from itsequilibrium position?

(c) How much additional work is required to stretch the spring to 0.5 mif it has already been stretched to 0.25 m from its equilibrium position?

Department of Mathematical SciencesInstructor: Markus SchmidmeierCalculus IISeptember 23, 2016 Name:

Quiz 5

1. Find the following integrals:

(a)

∫ 2

0

x2 + 2

x+ 1dx

(b)

∫x3 log(x) dx

(c)

∫sin(x)5 dx

P.T.O.

2 Calculus II, Quiz 5, September 23, 2016

2. Make a sketch of the region bounded by the graph of the function

y = ex,

the line x = log(5), the x-axis and the y-axis. Find the volume of thesolid that is generated by revolving the region about the y-axis. Whichmethod are you using?

Department of Mathematical SciencesInstructor: Markus SchmidmeierCalculus IISeptember 30, 2016 Name:

Quiz 6

1. Find the following integrals:

(a)

∫cos(x)6 sin(x)3 dx

(b)

∫x+ 1

x2 − 4dx

(c)

∫x+ 1

x2 + 4dx

P.T.O.

2 Calculus II, Quiz 6, September 30, 2016

2. Make a sketch of the region bounded by the graph of the function

y =1

x+ 1,

the x-axis, the y-axis and the line x = 3. Find the volume of thesolid that is generated by revolving the region about the y-axis. Whichmethod are you using?

Department of Mathematical SciencesInstructor: Markus SchmidmeierCalculus IIOctober 14, 2016 Name:

Quiz 7

1. Find the following integrals:

(a)

∫ ∞0

e−2x dx

(b)

∫ ∞0

1

x2 + 9dx

(c)

∫ ∞0

x

x2 + 9dx

P.T.O.

6 best quizzes: average: letter grade:

2 Calculus II, Quiz 7, October 14, 2016

2. Make a sketch of the region bounded by the graph of the function

y =1

(x− 1)2,

and the x-axis on the interval [2,∞). Find the volume of the solid thatis generated by revolving the region about the x-axis.

Department of Mathematical SciencesInstructor: Markus SchmidmeierCalculus IIOctober 21, 2016 Name:

Quiz 8

1. Several terms of a sequence {an}∞n=1 are given. Find the next twoterms of the sequence and state an explicit formula for the n-th termof the sequence.

(a) {1, 4, 7, 10, . . .}

(b) {−2, 4,−6, 8, . . .}

(c) {27, 9, 3, 1, . . .}

P.T.O.

2 Calculus II, Quiz 8, October 21, 2016

2. Find the limit for each of the following sequences or state that thelimit does not exist.

(a) {arctan(n)}

(b)

{7n3 + 21n2 + 19n+ 5

14n3 + 27n2 − 13n− 5

}

(c)

{(n+ 4

n

)n}