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1. Evaluate

lim x® 0    ___ Öx+1  - 1 x

1. -1
2. 0
3. 1/3
4. 1/2
2. The functions f(x) and g(x) are plotted in the graphs below.
Which of the following statements is true?
1. lim_{x® 2}[ f(x) +g(x) ] = 2
2. lim_{x® 2}[ f(x) +g(x) ] = 3
3. lim_{x® 2}[ f(x) +g(x) ] = ¥
4. lim_{x® 2}[ f(x) +g(x) ] does not exist
3. Given f(x) = 2Öx, L = 4, and x₀ = 4, find a value for d > 0 such that for all x satisfying 0 < |x-x₀| < d, the inequality

  | f(x) -L| < 0.1 holds.
1. 4.2025
2. 4
3. 0.2025
4. 0.1975
4. Evaluate

lim x® 0 sin2(4x) x2

1. 0
2. 4
3. 16
4. ¥
5. For what value of k is f(x) continuous at every x.

f(x) =  ì í î cosx x < 0  x2+k x ³ 0

1. f(x) cannot be continuous
2. k = -1
3. k = 0
4. k = 1
6. A rock is thrown vertically upward from the surface of the earth at a velocity of 24 m/sec. In the absence of air, the position of the rock is s = 24t-4.9t². How long would it take the rock to reach its highest point and how high would the rock go?
1. 2.4 sec and 29.4 m
2. 24 sec and 4.9 m
3. 2 sec and 9.6 m
4. 2.4 sec and 9.6 m
7. Based on the graph, which of these statements is true?

1. f(x) is differentiable and continuous at x = 2
2. f(x) is differentiable but not continuous at x = 2
3. f(x) is continuous but not differentiable at x = 2
4. f(x) is neither differentiable nor continuous at x = 2
8. The derivative of

y =  5x-2 x2+1

 is

(a)  15x2-4x+5 ( x2+1) 2         (b)  5+4x-5x2 ( x2+1) 2         (c)  5 2x        (d)  5 ( x2+1) 2

9. Find the derivative of y = sin²x+cos²x
1. 1
2. 2sin(x) +2cos(x)
3. 4sin(x) cos(x)
4. 0
10. The formula for the slope of the curve y = Öx - 3 for x > 0 is
1. 1/(6x)
2. 9x
3. 1/(2Öx)
4. 1/(2x)
11. Find the equation of the tangent to the curve y = (x-1)²+3 at x = 2
1. y = 5x-10
2. y = 2x
3. y = 4x-4
4. y = 2(x-1)
12. Given x²y³ = 7 find y'
1. Ö(6x)
2. ³Ö(7/x²)
3. -2y/(3x)
4. 7 - 2y/(3x)
13. A circular plate is heated in an oven. Its radius increases at the rate of 0.1 cm/min. At what rate is the plate's area increasing when the radius is 7 cm?
1. 14p
2. 49p
3. 1.4p
4. 0.7
14. Use a graphing calculator to graph f(x) = x⁴-x³+3x on [ -2,2] . Which of the following statements is true?
1. f'(x) = 0 for some x in [-1.5,-0.5]
2. f'(x) = 0 for some x in [-0.5,0.5]
3. f'(x) = 0 for some x in [0.5,1.5]
4. f'(x) = 0 for some x in [ 1.5,2]
15. The following is a graph of the derivative of a function y = f(x) .
Which of the following can we conclude from this graph?
1. f  is increasing on the interval (-¥,0]
2. f  has a local maximum at x = 0
3. f  is increasing on [ -2,2]
4. f  has an inflection point at x = 2
16. Suppose we are given the following information about a function y = f(x) :
1. f'(x) > 0 on the intervals (-¥,-1) and (1,¥)
2. f'(x) < 0 on the interval ( -1,1)
3. f''(x) > 0 on the interval (0,¥)
4. f''(x) < 0 on the interval (-¥,0)
Which of the following  could be the graph of y = f(x) ?
17. Find the number c in [2,8] that satisfies the Mean Value Theorem for f(x) = x+4/x
1. Ö13
2. Ö14
3. Ö15
4. 4
18. Find the area of the largest rectangle with lower base on the x-axis and upper vertices on the parabola y = 75-x².
1. Area = 5Ö3
2. Area = 25
3. Area = 250
4. Area = 500
19. The function f(x) = 3x⁴-12x³ has which of the following properties:
1. A maximum at (0,0) and a minimum at (-3,-81)
2. A minimum at (0,0) and a point of inflection at ( 2,-48)
3. A point of inflection at (0,0) and no maximum
4. A minimum at (0,0) and another minimum at (3,-81)
20. Evaluate òx^-5/4 dx
1. 4x^-1/4+C
2. -4x^-1/4+C
3. -5x^-9/4 /4+C
4. -5x^-1/4 /4+C
21. A car is accelerated from rest with a constant acceleration of 5 m/sec² for 10 seconds along a straight roadway. How far will the car have traveled after 10 seconds?
1. 50 meters
2. 125 meters
3. 250 meters
4. 500 meters
22. Evaluate

ò 6x2dx Ö 1-x3

( a) -4 Ö ___ 1-x3   + C        ( b)  -4 Ö 1-x3  + C        ( c)   -8 Ö 1-x3  + C       ( d)   -4x3 Ö 1-x3  + C

23. Graph the function f(x) = x²cos(x) on the interval [-4,4] . (Be sure to use radians). By examining the graph of f(x) , which of the following integrals is positive?
1. ò_-4^-3  x²cos(x) dx
2. ò₀¹  x²cos(x) dx
3. ò₂³  x²cos(x) dx
4. ò₃⁴  x²cos(x) dx
24. If ò₁²f(x) dx = 3 and ò₁⁵f(x) dx = 4, then ò₂⁵f(x) dx =
1. 0
2. 1
3. 3
4. 7
25. The area of the region between the curve y = x-x² and the x-axis is
1. 1/12
2. 1/6
3. 1/3
4. 1/2
26. For x in ( 0,[(p)/ 4]) , evaluate the following derivative:

d dx ò sin(x)  0 dt 1+t

( a)  1 1+sin(x)          (b)  1 1+cos(x)          ( c)  sin(x) 1+cos(x)          (d)  cos(x) 1+sin(x)

27. Which of the following integrals has the same value as

ò p/2 0 cos(x) 1+sin(x)  dx

(a)  ò 2 1 du u         (b)  ò p/2 1 cos(u) u  du        (c)  ò p/2 1 ( 1+cot u) du        (d)  ò 3 1 cot(u) du

28. The area bounded by y = x² and y = x+2 is described by the following integral:
1. ò_-1²( x+2-x²) dx
2. ò_-1²( x+1-x²) dx
3. ò_-1²( x+2-x²) dx
4. ò_-1²( x²-x-2) dx
29. Let R be the region bounded by y = x², the line x = 3 and the x-axis. The volume obtained when R is revolved about the y-axis can be obtained using the method of cylindrical shells. The volume can be found by the following integral.
1. 2pò₀³  x³dx
2. 2pò₀³  x²dx
3. pò₀³  x⁴dx
4. 2pò₀³  ( 3-x) x²dx
30. Let R be the region bounded by y = x², the line x = 3 and the x-axis. The volume obtained when R is revolved about the x-axis can be obtained using the disk method. The volume can be found by the following integral.
1. 2pò₀³  x⁴dx
2. pò₀³  x²dx
3. pò₀³  x⁴ dx
4. 2pò₀³  ( 9-x²) ²dx
31. Let R be the region bounded by y = x², the line y = 4 and the y-axis. By using the method of washers, find the volume of the solid when R is revolved about the x-axis.
1. pò₀²  ( 16-x⁴) dx
2. pò₀²  ( 4-x²) dx
3. pò₀²  ( 16-x⁴) ²dx
4. 2pò₀²  ( 4-x⁴) dx
32. Use a graphing calculator to find the length of the curve y = x² from x = 0 to x = 1
1. 0
2. 0.792
3. 1.479
4. 2.157
33. Set up the integral for the area of the surface generated by revolving the curve y = x², 1 £x£ 2, about the x-axis.
1. 2pò₁²  x²Ö{1+4x²} dx
2. 2pò₁²  x²Ö{1+x²} dx
3. 2pò₁²  Ö{1+4x²} dx

2pò₁² Ö{1+x²} dx