Calc BC exam

~(x/2)(e^-3x/4)

((-2x/3)e^-3x/4) + ((3/8)e^-3x/4) + c

If f(x)= (5-x)/(x^3+2) f'(x)=

(2x^3-15x^2-2)/(x^3+2)^2

~1/t√t

-2t^(-1/2) + c

Which of the following is the interval of convergence for the series E (x+2)^n/2^n

-4<x<0

Let H(x) be an antiderivative of x^3+sinx / x^2+2 If H(5)=pi H(2)=

-5.867

The graph of the function f is shown above If g is the function defined by g(x)= ~2 x f(t) what is the value of g(10) times g'(10)

-5/2

If f(x)=cos^2(3x-5) f'(x)=

-6sin(3x-5)cos(3x-5)

The velocity vector of a particle moving in the xy-plane has components dx/dt= sin(t^2) dy/dt= e^cost At time t=4, the position of the particle is (2,1). What is the y-coordinate of the position vector at time t=3?

0.590

Which of the following is a power series expansion of e^x+e^-x/2?

1 - x^2/2! + x^4/4! - x^6/6! + ... + ((-1)^n x^2n)/(2n!)

A particle moves in the xy-plane so that its position for t>= is given by the parametric equations x=ln(t+1) and y=kt^2, where k is a positive constant. The line tangent to the particle's path at the point where t=3 has slope 8. What is the value of k?

1/3

~0 5 √((5-x)/5)

10/3

The table above(#21) gives the level of a person's cholesterol at different times during a 10-week treatment period. What is the average level over this 10-week period obtained by using a trapezoidal approximation with the subintervals [0,2] [2,6] [6,10]?

193

The slope of the line tangent to the graph of y=xe^x at x=ln2 is

2ln2+2

If f(x)= E x^2n/n! f'(x)=

2x + 2x^3 + x^5 + x^7/3 + ... + 2nx^2n-1/n!

If x^2+xy-3y=3, then at the point (2,1) dy/dx=

5

The number of students in a cafeteria is modeled by the function P that satisfies the logistic differential equation dP/dt= 1/2000P(200-P), where t is the time in seconds and P(0)=25. What is the greatest rate of change, in students per second, of the number of students in the cafeteria?

5

~(3x+1)/(x^2-4x+3)=

5ln[x-3] - 2ln[x-1] + c

The twice differentiable functions f, g and h have second derivatives given above(#86) Which of the functions f, g and h have a graph with exactly two points of inflection?

f and g only

Let f be a twice-differentiable function for all real numbers x. Which of the following additional properties guarantees that f has a relative minimum at x=c?

f'(c)=0 and f"(c)>0

The derivative of the function f is given by f'(x)=e^-xcos(x^2) What is the minimum value of f(x) for -1<x<1

f(-1)

What is the radius of convergence of the Maclaurin series for 2x/1+x^2?

infinite

The continuous function f is positive and has domain x>0. If the asymptotes of the graph of f are x=0 and y=2 Which of the following statements must be true?

lim as x->0+ f(x)= infinite and lim as x-> infinite f(x)=2

Look at graphs for #15. Which statement is false?

lim as x->1 (f(x)g(x+1)) does not exist

Look at graph on #6 Which of the following is true?

lim as x->a of f(x) does not equal f(a)

Which of the following is a slope field for dy/dx= x^2+y^2?

look for graph where slope increases as y increases

The graph of the function f is shown above(#81) for -2<x<2 Which of the following could be the grapph of an antiderivative of f?

looks like wide and slightly wavy x^3

Let f be the function given by f(x)=2cosx+1. What is the approximation for f(1.5) found by using the line tangent to the graph of f at x=pi/2?

pi-2

To what number does the series E (-e/pi)^k converge?

pi/(pi+e)

Let f be the function with f(0)=1/pi^2, f(2)=1/pi^2, and derivative given by f'(x)=(x+1)cos(pix). How many values of x in the open interval (0,2) satisfy the condition of the MVT for the function f on the closed interval [0,2]?

two

The function f is increasing on the interval [1,3] and nowhere else. The first derivative of f, f' is continuous for all real numbers. Which of the following could be a table of values for f'(x)?

x 0 1 2 3 4 y -1 1 2 1 -2

The position of a particle moving in the xy-plane is given by the vector {4t^3,y(2t)}, where y is a twice-differeniable function of t. At time t=1/2, what is the acceleration vector of the particle?

{12,4y"(1)}

The base of a solid is the region bounded by a portion of the graph of y=sin(pi/2x) and the x-axis, as shown in the figure above(#83) For the solid, each cross section perpendicular to the x-axis in a rectangle of height 3. Which of the following expectations gives the volume of the solid?

~0 2 3sin(pi/2x)

The length of the curve y=sin(3x) from x=0 to x=pi/6 is given by

~0 pi/6 √1+9cos^2(3x)

Let S be the region in the first quadrant bounded above(#89) by the graph of the polar curve r=cos(theta) and bounded below by the graph of the polar curve r=2theta The two curves intersect when theta=0.450 What is the area of S?

0.243

The graph of a function f, consisting of three line segments, is shown above(#79) The function f is defined on the closed interval [0,6] Let g(x)= ~2 x f(t) What is the maximum value of g(x) for 0<x<6?

1

A cube with edges of length x centimeters has volume V(x)=x^3 cubic centimeters. The volume is increasing at a constant rate of 40 cubic centimeters per minute. At the instant when x=2, what is the rate of change of x, in centimeters per minute, with respect to time?

10/3

Let y=f(x) be the solution to the differential equation dy/dx= x-y with initial condition f(2)=8. What is the approximation for f(3) obtained by using Euyler's method with two steps of equal length, starting at x=2?

15/4

The position of an object moving along a path in the xy-plane is given by the parametric equations x(t)=5sin(pit) y(t)=(2t-1)^2 The speed of the particle at time t=0 is

16.209

If g is a twice-differentiable function, where g(1)=0.5 and lim as x->infinite g(x)=4 then ~1 infinite g'(x)=

3.5

If the infinite series S= E (-1)^n+1 (2/n) is approximated by Pk= E (-1)^n+1 (2/n) What is the least value of k for which the alternating series error bound guarantees that [S-Pk}= 3/100

68

If ~4 -10 g(x)=-3 and ~4 6 g(x)=5 then ~-10 6 g(x)=

8

If the average value of a continuous function f on the interval [-2,4] is 12 what is ~-2 4 f(x)/8

9

Which of the following are equal to -1? I. lim x->0- [x]/x II. lim x->3 (x^2-7x+12)/(3-x) III. lim x->infinite (1-x)/(1+x)

I and III only

Which of the following statement about the series E 1/2^n-n is true?

The series converges by the limit comparison to the geometric series E 1/2^n

If f(x)=3x^2+2x f'(x)=

lim as h->0 (3(x+h)^2+2(x+h))-(3x^2+2x) / h