MATH 221 Solutions to Final Exam Review Exercises
Part I
1. a)
b)
c)
d)
e)
f)
g)
2. a)
b)
c) Ignore problem 2c.
3. a)
b) =32/81
8/3
e)
Part II
1. a) b) x = -2.
2. a) Point = (-1,3), Slope = 3(-1)2 – 4 = -1 . Equation (y-3) = (-1)(x+1)
b) x = 1, -1. Points (-1,3) and (1,-3)
c) Slope of
perpendicular = 1. 3x2 – 4 = 1.
.
Points
d) (2,3) is not on the graph of y = x2. Let (x,x2)
be a point on the graph whose tangent line passes through (2,3). Then the slope
of the tangent is given by 2x and by . Setting these equal yields x = 3 and x = 1. The respective slopes are 6 and 2. The
equations are (y-3) = 6(x-2) and (y-3) = 2(x-2).
3. a) Equation of line y = 2-x. Curves cross at x = -2 and at x = 1.
Area =
b) Area =
4. 486 square inches.
5. a) .
C = 3.
b) ,
,
C = 1, D = 3.5.
6. a)
Critical points -3, 4, 1 Local Max at -3, Local Min at 1
b) First volume =
Second Volume =
7. Removable discontinuity at x = -2, Removable discontinuity at x = -1, Infinite or Essential discontinuity at x = 2.
8. a)
Area = 1/2
b) i)
ii)
9. a)
Point (1,1), Slope = -1/2. Equation
b) , x = 1, -1. Points (1,4), (-1,-4).
Slope = 6
Equations (y-4) = 6(x-1) and (y+4) = 6(x+1)
c)
, x = 1, -3
Points (1,3), (-3, 3), Slopes 4, -4
Equations (y-3) = 4(x-1) and (y-3) = -4(x+3)