spring break calc assignment

The graph of f is shown above for 0<x<4. What is the value of the integral from 0 to 4 of f(x) dx

0

What is the average value of y = root cos x on the interval 0<x<pi/2

0.763

the integral from 1 to 4 of t^-3/2 dt =

1

Let g be a continuously differentiable function with g(1) = 6 and g'(1) = 3. What is the limit as x goes towards 1 of the integral of g(t) dt/g(x) -6?

2

Let f be a function having derivatives of all orders for x > 0 such that f(3)=2, f'(3)= -1, f''(3) = 6, and f'''(3)= 12. Which of the following is the third-degree Taylor polynomial for f about x = 3 ?

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

The graph of the piecewise linear function f is shown above. What is the value of the integral of (3f(x)+2) dx ?

27.5

The graph of f' , the derivative of a function f, consists of two line segments and a semicircle, as shown in the figure above. If f(2)= 1, then f (-5) =

2pi-2

If y = sin^3 x then dy/dx=

3sin^2xcosx

If f'(x) >0 for all real numbers x and the integral from 4 to 7 of f(t)dt = 0, which of the following could be a table of values for the function f ?

4, -4 5, -2 7, 5

The fuel consumption of a car, in miles per gallon (mpg), is modeled by F(s) = 6e^(s/20-s^2/2400), where s is the speed of the car, in miles per hour. If the car is traveling at 50 miles per hour and its speed is changing at the rate of 20 miles/hr squared, what is the rate at which its fuel consumption is changing?

4.299 mpg per hour

The Maclaurin series for the function f is given by f(x)= series from 0 to infinity (-x/4)^n. What is the value of f(3)?

4/7

Let y = f(x) be the solution to the differential equation dy/dx = x-y with initial condition f(1)= 3. What is the approximation for f (2) obtained by using Euler's method with two steps of equal length starting at x = 1 ?

7/4

The figure above shows the graphs of the polar curves r = 2cos(3theta) and r = 2. What is the sum of the areas of the shaded regions?

9.425

The graph of f', the derivative of the function f, is shown above. Which of the following statements must be true? I. f has a relative minimum at x = -3. II. The graph of f has a point of inflection at x = -2. III. The graph of f is concave down for 0<x<4

I and III only

Which of the following series converge?

I and III only

The function h is differentiable, and for all values of x, h(x) = h(2-x). Which of the following statements must be true? I. integral from 0 to 2 of h(x) dx > 0 II. h'(1) = 0 III. h'(0)=h'(2)=1

II only

The power series from 0 to infinity of a sub n (x-3)^n converges at x = 5. Which of the following must be true?

The series converges at x = 2.

If P(t) is the size of a population at time t, which of the following differential equations describes linear growth in the size of the population?

dP/dt = 200

Let k be a positive constant. Which of the following is a logistic differential equation?

dy/dt= ky(1-y)

Let f be the function defined by f(x)= square root of the absolute value of x-2 all values of x. Which of the following statements is true?

f is continuous but not differentiable at x = 2.

The function f, whose graph is shown above, is defined on the interval -2<x<2. Which of the following statements about f is false?

f is differentiable at x = 0.

If the function f is continuous at x = 3, which of the following must be true?

f(3)= lim as x goes to 3 from left of f(x) = lim as x goes to 3 from the right of f(x)

The derivative of a function f is increasing for x < 0 and decreasing for x > 0. Which of the following could be the graph of f ?

graph is only in quadrants 2 and 4, begins concave up, intersects at the origin, and ends concave down

The graph of a differentiable function f is shown above. If h(x)= integral from 0 to x of f(t) dt, which of the following is true ?

h(6)<h'(6)<h''(6)

Which of the following integrals gives the length of the curve y = ln x from x = 1 to x = 2 ?

integral from 1 to 2 of the square root of 1+1/x^2 dx

the integral from 0 to 1 of (5x+8)/(x^2+3x+2) dx is

ln(18)

What is the radius of convergence of the series from 0 to infinity of (x-4)^2n/3^n

root 3

For x > 0, the power series 1-x^2/3!+x^4/5!-x^6/7!+...+ (-1)^n x^2n/(2n+1)!+...converges to which of the following?

sinx/x

If arcsin(x) = lny, then dy/dx=

y/(square root of 1-x^2)

The line y = 5 is a horizontal asymptote to the graph of which of the following functions?

y= 20x^2-x/(1+4x^2)

NO CALC SECTION!

you can not use your calc for 1-28

CALC SECTION!

you can use your calc now for 76-92

The points (- 1, -1) and (1, -5) are on the graph of a function y = f(x) that satisfies the differential equation dy/dx = x^2+ y. Which of the following must be true?

( - 1, -1) is a local maximum of f.

For -1.5 <x< 1.5, let f be a function with first derivative given by f'(x)= e^(x^4-2x^2+1) -2. Which of the following are all intervals on which the graph of f is concave down?

(- 1.5, -1) and (0, 1)

The position of a particle moving in the xy-plane is given by the parametric equations x(t)= t^3-3t^2 and y(t)= 12t-3t^2. At which of the following points (x, y) is the particle at rest?

(-4, 12)

Let f and g be the functions given by f(x) = e^x and g(x) = x^4. On what intervals is the rate of change of f(x) greater than the rate of change of g(x)?

(-infinity, 0.831), and (7.384, infinity)

The function f is defined by f(x) = x/x+2. What points (x,y) on the graph of f have the property that the line tangent to f at (x,y) has slope 1/2?

(0,0) and (-4,2)

Let R be the region in the first quadrant bounded above by the graph of y = ln(3-x), for 0<x<2. R is the base of a solid for which each cross section perpendicular to the x-axis is a square. What is the volume of the solid?

1.029

What is the slope of the line tangent to the polar curve r = 1+2sintheta at theta = 0?

1/2

Using the substitution u= x^2-3, the integral from -1 to 4 of x (x^2-3)^5 dx is equal to which of the following ?

1/2 integral from -2 to 13 of u^5 du

For what values of p will both series 1/n^2p and (p/2)^n converge?

1/2<p<2 only

integral from 1 to infinity of xe^-x^2 dx is

1/2e

A particle moves along a line so that its acceleration for t ≥ 0 is given by a(t)= t+3/root t^3 +1. If the particle's velocity at t = 0 is 5, what is the velocity of the particle at t = 3 ?

11.710

A tank contains 50 liters of oil at time t = 4 hours. Oil is being pumped into the tank at a rate R(t) , where R(t) is measured in liters per hour, and t is measured in hours. Selected values of R(t) are given in the table above. Using a right Riemann sum with three subintervals and data from the table, what is the approximation of the number of liters of oil that are in the tank at time t = 15 hours?

114.9

If the series from 1 to infinity of a sub n converges, and a sub n >0 for all n, which of the following must be true?

the series of a sub n/n converges

Let f be a function that is twice differentiable on -2<x<2 2 and satisfies the conditions in the table above. If f(x)= f(-x), what are the x-coordinates of the points of inflection of the graph of f on -2<x<2?

x = -1 and x = 1

Let f be a differentiable function such that the integral of f(x)sinx dx = -f(x)cosx + integral of 4x^3cosx dx. Which of the following could be f(x) ?

x^4