AP Calculus Semester Exam WITH 100% Verified Answers.

AP Calculus Semester Exam WITH 100% Verified Answers. the graph of f is shown, for which of the following values of x is f'x positive and increasing? - ANSWERS e let f b a function that is continuous on the closed interval [2,4] with f(2)=10 and f(4)=20. Which of the following is guaranteed by the Intermediate Value Theorem? - ANSWERS f(x)=13 has at least one solution in the open interval (2,4) the graph of (e^tanx)-2 crosses the x-axis at one point in the interval [0,1]. What is the slope of the graph at this point? - ANSWERS 2.961 a particle moves along the x axis. the velocity of the particle at time t is given by v(t), and the acceleration of the particle at time t is given by a(t). which of the following gives the average velocity of the particle from t=0 to t=8 - ANSWERS 1/8!v(t)dt from 0 to 8 the graph of f' is shown above. which of the following statements must be true? bell graph - ANSWERS I and III only water is pumped into a tank at a rate of r(t)=30(1-e^-.16t) gallons per minute. if the tank contained 800 gallons of water when the pump was turned on, how much water to the nearest gallon is in the tank after 20 minutes? - ANSWERS 1220 gallons if f'= the square root of (x^4+1)+x^3-3x, then f has a local maximum at x= - ANSWERS .350 the graph above gives the velocity in ft/sec of a car for 0t8, where t is the time in seconds. Of the following, which is the best estimate of the distance traveled by the car from t=0 until the car comes to a complete stop? - ANSWERS 210ft for -1.5x1.5, 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? - ANSWERS (-1.5,-1) and (0,1) the graph f' is shown in the figure above. the function f has a local maximum at x=?mountain looking graph crosses the x axis at x=1 - ANSWERS -3 if f'0 for all real numbers x and the integral from 4 to 7 f(t)dt=0, which of the following could be a table of values for the function f? - ANSWERS x f(x) 4 -4 5 -2 7 5 the graph of f'' is shown above for -2x4, what are all intervals on which the graph of the function f is concave down? - ANSWERS -2x-1 ND 1X3 a person whose height is 6 feet is walking away from the base of a streetlight along a straight path at a rate of 4 ft/sec. IF the height of the streetlight is 15 feet, what is the rate at which the person's shadow is lengthening? - ANSWERS 2.667 ft/sec a particle moves along a line so that its acceleration for t0 is given by a(t)=(t+3)/(t^(3)+1)^1/2. if the particles velocity at t=0 is 5, what is the velocity of the particle at t=3? - ANSWERS .713 let f be a function such that the integral from 6 to 12 f(2x)dx =10. Which of he following must be true? - ANSWERS the integral from 12 to 24 f(t)dt=20 let f be a polynomial function with values of f' at selected values of x given in the table above. which of the following must be true for -2x6? - ANSWERS the graph of f has at least two points of inflection a particle moves along a straight line so that at time t0 the position of the particle is given by s(t), the velocity is given by v(t), and the acceleration is given by a(t). Which of the following expressions gives the average velocity of the particle on the interval [2,8]? - ANSWERS [s(8)-s(2)]/6 if sin(1/x^2 +1) is an antiderivative for fx, then the integral from 1 to 2 of fxdt = - ANSWERS -.281 the function is differentiable and increasing for all real numbers x, and the graph of f has exactly one point of inflection. Of the following, which could be the graph of f'? - ANSWERS the graph with the sharp point the table above gives selected values of a function f. THe function is twice differentiable with f'' 0. What is the value of f'(3) - ANSWERS .7 really fun waterslide figure above shows the graph f', for -6x8. which best describes the graph of f on the same interval? - ANSWERS 1 relative minimum, 1 relative maximum, 3 points of inflection The regions A,B, and C in the figure above are bounded by the graph of the function f and the x-axis. The area of region A is 14, the area of region b is 16, and the area of region c is 50. What is the average value of f on the interval [0,8] - ANSWERS 6 let f and g be continuous functions such that the integral from 0 to 6 fxdx=9, the integral from 3 to 6 fxdx=5 and the integral from 0 to 3 gxdx=7. What is the value of the integral from 0 to 3 of .5fx-3gx dx? - ANSWERS -19 a particle moves along the x axis so that its velocity at time t0 is given by (t^(2)-1)/(t^(2) +1). what is the total distance traveled by the particle from t=0 to t=2? - ANSWERS .927 the graph of the differentiable function f is shown in the figure above. let h be defined by hx= the integral of ftdt. Which of the following correctly orders h(2), h'(2), and h''(2)? - ANSWERS h''2h'2h2 a differentiable function f has the property that f'x 3 for 1x8 and f(5)=6. What is true? - ANSWERS I and II only a particle moves along a line so that its velocity is given by vt=-t^3+2t^2+2^-t for t0. For what values of t is the speed of the particle increasing? - ANSWERS (0.177, 1.256) and (2.057, infinity) let f be a function defined for all real numbers x such that F' 0 and F''0. Which of the following could be a table of values for F? - ANSWERS x Fx 1 -3 2 -1 3 3 4 19 if xsinx=y, then dy/dx= - ANSWERS sinx=xcosx let f be the function given by fx = 300x-x^3, on what intervals is the function f increasing - ANSWERS [-10,10] the integral of secxtanxdx= - ANSWERS secx+c fx=7x-3+lnx, then f(-1)= - ANSWERS 8 the graph of the function is shown above, which of the following statements it false? discontinuous graph of f - ANSWERS limfx x-4 exists a particle moves along the x-axis. the velocity of the particle at time t is 6t-t^2. What is the total distance traveled by the particle from time t=0 to t=3? - ANSWERS 18 y=(x^3 - cosx)^5, then y' = - ANSWERS 5(x^3 -cosx)^4(3x^2+sinx) a tank contains 50 liters of oil at time t = 4 hours. OIl is being oumoed into the tank at a rate r(t). Do a right Riemann sum with three subintervals and solve for the number of liters of oil that are in the tank at t=15 hrs - ANSWERS 114.9