Key to Practice Midterm II

Problem 1

A.  False, it could be (-2,2), [-2,2), [-2,2] or [-2,2]

B.  Falset + 1 = t has no solution

C.  True, since |r| represents the distance from the origin which is well defined.

Problem 2

A.  R = 1/5, Interval = [-2/5,0]

B.  R = 1/5, Interval = [-2/5,0)

C.  R = 1/5, Interval = [-2/5,0]

Problem 3

sum (-1)ⁿ x²ⁿ⁺² /(n+1)

Interval= (-1,1)

Problem 4

A.  sum (-1)ⁿ x²ⁿ⁺¹ /n!(2n+1)

B.  sum (-1)ⁿ /n!(2n+1)

C. solving 1/(n + 1)!(2n+1) < .00001 gives n = 7.  

Problem 5

Hor:   (16,0)

Ver:  (0,16)

Problem 6

A. (0,2),(0,0), (-sqrt3/4,1/4),(-sqrt3/4,-1/4)

B.  4int from 0 to pi/12(4sin2t)² dt + 4int from pi/12 to pi/4 (2)² dt

Problem 7

1

Problem 8

-sqrt2 i + sqrt2 j and sqrt2 i - sqrt2 j

Problem 9

r = 1.78/(1 - .98cos(theta))

Problem 10

-25 - 17y + 7z =- 53