Multivariable Calculus III Practice Midterm 1
Prof. Fedorchuk
No calculators will be allowed on the exam.
1.
(5 points ) If v w = 1, 1, 1 and v w = 2, nd the angle between
v and w.
2. (10 points ) For
Multivariable Calculus Practice Midterm 2 Solutions
Prof. Fedorchuk
1.
2
(10 points ) Let f (x, y, z ) = xz + eyx .
a. (4 pts ) Compute the gradient f .
b. (3 pts ) Find the directional derivative
D
1
Multivariable Calculus Practice Midterm 2
Prof. Fedorchuk
1.
2
(10 points ) Let f (x, y, z ) = xz + eyx .
a. (4 pts ) Compute the gradient f .
b. (3 pts ) Find the directional derivative
D
1
0, 2 ,
3
Multivariable Calculus Practice Midterm 2
Prof. Fedorchuk
1.
(10 points ) Compute the arc length of the curve
r(t) =
43
t, t 2 , t2 ,
3
on the interval 1 t 3.
1
Solution: We have r (t) = 1, 2t 2 , 2t
Multivariable Calculus Practice Midterm 2
Prof. Fedorchuk
1.
(10 points ) Compute the arc length of the curve
r(t) =
43
t, t 2 , t2 ,
3
on the interval 1 t 3.
2.
(10 points ) Reparametrize the curve r
MULTIVARIABLE CALCULUS PRACTICE MIDTERM 1 SOLUTIONS
1.
(5 points ) If v w = 1, 1, 1 and v w = 2, nd the angle between v and w.
Solution: Let be the angle in question. By using the formula for the magn
COMM 2202
Fall 2015
Assignment #1
Due: At the beginning of your class,
Tuesday October 13th for T-TH classes
Wednesday October 14th for M-W classes
Note: This assignment may be done in groups of up to