Calculus BC

1

C. x^2/2 - 5/x + C

2. What is the slope of the line tangent to the graph of y = ln(2x) at the point where x = 4?

B. 1/4

3. \

D. 2

4\.

E. 1/3 ln |x-2/x-5| + C

5. \

C. I and II only

6. The infinite series blah blah

E. the series diverges

7. \

A. -7

8\.

B. 13/12

9. The function f has a first derivative given by f’(x) = x(x-3)^2(x+1). At what values of x does f have a relative maximum

A. -1 only

10. \

B. -2/e^2+2e

11. \

E. nonexsistent

12. Let f be the function given by f(x) = 9^x. If four subintervals of equal length are used, what is the value of the right Riemann sum approx. for Int 0-2 f(x)dx?

C. 60

13. A rectangular area is to be enclosed by a wall on one side and fencing on the other three sides. If 18 meters of fencing are used, what is the maximum area that can be enclosed?

E. 81/2m^2

14. Let P(x) = 3-3x^2 +6x^4 be the fourth-degree Taylor polynomial for the function f about x = 0. What is the value of f(4)(0)?

E. 144

15. Suppose ln x - ln y -4, where y is a differentiable function of x and y = 4 and x = 4. What is the value of dy/dx when x = 4?

B. 1/5

16. \

A. k^3/6

17. Which of the following is the Maclaurin series for e^3x

E. 1 + 3x

18. \

B. 1/9

19. For what values of x does the graph of y = 3x^5 + 10x^4 have a point of inflection?

B. x = -2 only

20. if f’(x) = (x-2)^3(x^2-4)/16 and g(x) = f(x^2-1), what is g’(2)?

B. 5/4

21. \

D. 2 sqrt5 + 2 sqrt2 + 2

22. What is the interval of convergence of the power series …

B. 1

23. What is the particular solution to the differential equation dy/dx = xy^2 with the initial condition y(2) = 1?

D. y = 2/6-x^2

24\.

C. III only

25. what is the slope of the line tangent to the polar curve r = cos 0- at the point where 0- = pi/6?

B. -1/sqrt3

26. \

A. 1/2sqrtx(1+x)

What is the cofficient of x^2 in the taylor series for sin^2x about x = 0

D. 1

The function h is given by h(x) = x^5+3x-2 and h(1)=2. If h^-1 is the inverse of h, what is the value of (h^-1)’(2)?

B. 1/8

76. The figure above shows the graph of the differentiable function f for

C. u

77. The # of antibodies y in a patient’s blood stream at time t is increasing according to a logistic differential equation. Which of the following ?

E. dy/dt = 0.025y(5000-y)

78. What is the area of the region enclosed by the graphs of y = 1/1+x^2 and y = x^2 - 1/3?

C. 1.582

79. A vase

E. 80.115

80. \

A. p’(-2) < 0

81. At time t = 0 years, a forest preserve has a population of 1500 deer.

D. 10,141

82. The figure above shows the graph of f’

A. 1 relative min, 1 relative max, and 3 points of inflection

83. The table above gives values of f’ the derivative of a function f. If f(1) = 4, what is the approx. to f(2) obtained by using Euler’s method with a step size of 0.5?

C. 4.35

84. A sphere is expanding in a such a way

B. 16cm^3/sec

85. for t >= 0, the components of the velocity of a particle moving in the xy-plane are given

C. 0.495

86. the table above

B. 49

87. if 0 < Bn < An for n >= 1

B. if converges

88. a particle moves along

B. The velocity of the particle is 0for some t between t = 0 and t = 1.

89. The function f is given by f(x) =

E. 2.694

90. A particle moves along a line so that its velocity is given

E. (0.177, 1.256) and (2.057,inf)

91. line l is tangent

D. 2.798

92\.

A. 63