Name: Solutions
Math 2217 - Spring 2016 - Quiz 1 - Solutions
Problem 1. Let P = (1, 0, 6) and Q = (3, 2, 3), and v = PQ.
(A) Write v in component form.
(B) Write v as a linear combination of i, j, and k.
(C) Graph v.
Solution to Question 1.
(A) v = h2, 2,
Math 2217: Calculus III
Exam 2 Review
Math 2217 - Spring 2016 - Examination 2 Review Problems - Solutions
I. Calculations
Problem 1. Compute each limit:
(A)
x6 y4
(x,y )(0,0) x 4 + y 4
(B)
y x +2
(x,y )(3,1) (x 3)2 + (y 1)4
lim
lim
x 2y
(C)
lim
where f is
Math 2217: Calculus III
Exam 2 Review
Math 2217 - Spring 2016 - Examination 2 Review Problems
I. Calculations
Problem 1. Compute each limit:
(A)
x6 y4
(x,y )(0,0) x 4 + y 4
(B)
y x +2
(x,y )(3,1) (x 3)2 + (y 1)4
(C)
x 2y
where f is differentiable and f (1
Math 2217: Calculus III
Exam 2 Review
Math 2217 - Spring 2016 - Examination 2 Review Problems - Solutions
II. Conceptualization - These problems are not as straight forward as the others on this review. You
should expect one or maybe two problems like thi
Name: Solutions
Math 2217 - Spring 2016 - Quiz 4 - Solutions
Problem 1. A baseball is thrown off of the roof of a six story building with an initial speed of 29.4 meters
per second (= 3 9.8) at angle of 30 relative to the horizontal. If the ball is thrown
Name: Answers
Math 2217 - Spring 2016 - Quizzes 6, 7, and 8 - Answers
Quiz 6:
Problem 1. (4 Points): Consider the function of two variables f (x, y ) = sin(x 2 y).
(A) Calculate
2
f f 2f 2f
, ,
,
, f ,
x y x 2 y 2 x y
and
2f
.
y x
(B) Determine the slope
Name: Solutions
Math 2217 - Spring 2016 - Quiz 3 - Solutions
Problem 1.
(A) Let P = (1, 4/3, 1) be a point given in cylindrical coordinates. Convert P to rectangular corrdinates
and to spherical coordinates.
(B) Consider the equation of the surface given
Name: Solutions
Math 2217 - Spring 2016 - Quiz 10 - Solutions
Problem 1. (2 Points): Consider the R region bounded by the polar curve r = 2 + cos(). Set up, but do
not evaluate, an integral for the area of R.
Solution to Question 1.
Z
2
2+cos( )
Z
r dr d
Name:
Math 2217 - Spring 2016 - Quiz 2 - Solution
Problem 1. Let u = h3, 1, 1i, v = h1, 0, 2i, and w = h0, 3, 4i.
(A) What is the area of the parallelogram with adjacent sides v and w?
(B) What is the volume of the paraellelepiped with adjacent sides u, v
Name: Solutions
Math 2217 - Spring 2016 - Quiz 9 - Solutions
Problem 1. (5 Points): Consider the R region bounded by x = (y 2)2 4 and y = x + 4. Compute the
area of R.
Solution to Question 1. Before integrating, we need to better understand R. We find the
Math 2217: Calculus III
Exam 1 Review
Math 2217 - Spring 2016 - Examination 1 Review Problems
I. Calculations - Determine the scalar, vector, point, equation, or system of equations for each problem
below.
Problem 1. Let u = h2, 5, 4i and v = h5, 3, 1i. D