Calc Multiple Choice

# Calc Multiple Choice

1.  Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = sin(x), the x-axis, x = 0, and x = π (4 points)

2.  Suppose  , and  , find the value of  . (4 points)

 16 18 8 32
3.  Evaluate the integral  . (4 points)

 -2 0 2 4
4.  Use your graphing calculator to evaluate to three decimal places the value of  . (4 points)

 3.771 3.636 1.571 1.111
5.   (4 points)

 True False
1.  Find the average value of f(x)=e2x over the interval [2, 4]. (4 points)

 1463.18 731.59 1517.78 23.6
2.  Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = 2t + sin(t) and v(0) = 4. (4 points)

 v(t) = t2 + cos(t) + 3 v(t) = 2 + cos(t) + 1 v(t) = t2 – cos(t) + 5 v(t) = t2 + sin(t) + 4
3.  Find the distance, in feet, a particle travels in its first 4 seconds of travel, if it moves according to the velocity equation v(t)= -t2 + 4 (in feet/sec). (4 points)

 16 12
4.  For an object whose velocity in ft/sec is given by v(t) = -t2 + 4, what is its displacement, in feet, on the interval t = 0 to t = 3 secs? (4 points)

 7.67 -3 -0.33 3
5.  A girls throws a tennis ball straight into the air with a velocity of 64 feet/sec. If acceleration due to gravity is -32 ft/sec2, how many seconds after it leaves the girl’s hand will it take the ball to reach its highest point? Assume the position at time t = 0 is 0 feet. (4 points)

 4 secs 2 secs 1 sec Cannot be determined
1.  Which of the following is the general solution of the differential equation  ? (4 points)

 y2 = x2 + C x2 – y2 = C y2 = 4×2 + C y2 = 8×2 + C
2.  The slope of the tangent line to a curve at any point (x, y) on the curve is  . What is the equation of the curve if (3, 1) is a point on the curve? (4 points)

 x2 + y2 = 8 x + y = 8 x2 – y2 = 8 xy = 8
3.  The particular solution of the differential equation  for which y(0) = 60 is (4 points)

 y = 60e2t y = 60 e0.5t y = 59 + et y = 30et
4.  The temperature of a roast varies according to Newton’s Law of Cooling:  , where T is the water temperature, A is the room temperature, and k is a positive constant.

If a room temperature roast cools from 68°F to 25°F in 5 hours at freezer temperature of 20°F, how long (to the nearest hour) will it take the roast to cool to 21°F? (4 points)

 1 9 12 24
5.  Find the specific solution of the differential equation  with condition y(-2) = e. (4 points)

 None of these
1.  Choose the appropriate table for the differential equation  . (4 points)

 x 0 0.5 2 0 undefined
 x 0 0.5 2 undefined -1 undefined
 x 0 0.5 2 0 -3 0
Cannot be found without solving the differential equation
2.  A differential equation that is a function of x only (4 points)

 will produce a slope field with parallel tangents along the diagonal will produce a slope field that does not have rows or columns of parallel tangents will produce a slope field with rows of parallel tangents will produce a slope field with columns of parallel tangents
3.  The differential equation  . (4 points)

I.will have a slope field with negative slopes in quadrant I II.will have a slope field with positive slopes in all quadrants III.will produce a slope field with columns of parallel tangents

 I only II only III only None of these
4.  Which of the following differential equations is consistent with the following slope field?

(4 points)

5.  The differential equation  . (4 points)

I. produces a slope field with horizontal tangents at y = 4 II. produces a slope field with horizontal tangents at x = 0 III. produces a slope field with vertical tangents at x = 0 and y = 4

 I only II only I and II III only
1.  Which of the following values would be obtained using 10 inscribed rectangles of equal width (a lower sum) to estimate  ? (4 points)

 0.285 0.385 1.38 2.31
2.  Which definite integral approximation formula is  ? (4 points)

 Left rectangles Right rectangles Average value Trapezoidal rule
3.  The estimated value of  , using the trapezoidal rule with 4 trapezoids is (4 points)

 2.75 5.5 1.88 3.75
4.  Given the table below for selected values of f(x), use 6 trapezoids to estimate the value of

. (4 points)

 x 1 3 4 6 7 9 10 f(x) 4 8 6 10 10 12 16

________________________

5.  Function f(x) is positive, increasing and concave down on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of .  Which one of the following statements is true? (4 points)

 Trapezoidal rule value < Left sum < Right sum Left sum < Trapezoidal rule value < Right sum Right sum < Trapezoidal rule value < Left sum Cannot be determined without the x-values for the partitions