Math 215 Practice Exam 1, Study notes of Algebra

Download Math 215 Practice Exam 1 and more Study notes Algebra in PDF only on Docsity!

Name:

Math 215 Practice Exam 1

1. Given the vectors v = 〈− 6 , 7 , 2 〉 and w = 〈 4 , − 2 , 5 〉, find

a) (4 points) ‖v + w‖

b) (4 points) 2v · w

c) (6 points) v × w.

(Answers: a)

78, b) -56, c) 〈 39 , 38 , − 16 〉)

2. (15 points) Find the equation of the tangent line to f (t) =

cos(arctan(t)),

t 3

• 1

t − 2

at the point (

2 / 2 , −2). (Answer: <

2 / 2 , − 2 > +t < −

2 / 4 , − 5 > is one

such equation)

4. Find the arc length of the portion of the curve

f (t) = 〈t 2 , t cos(t) − 2 sin(t/2) cos(t/2), cos(t) + t sin(t)〉

from t = 0 to t =

π

2

. (Answer: π 2

5. Determine

lim t→∞

3 arctan(t) − π/ 2 , t sin

π

t

t^2 + ln(π)

t^2

)t 2 〉

.

You may assume t > 0. (Answer: 〈π, π, π〉)