The graph of f the derivative of a function f consists of two line segments and a semicircle

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

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Hello everyone. So this question the graph is given what it does. Along with this the given information Is F two is equal to one in this we have to find the value of f minus faith. Okay so from the figure we can see that this graph can be divided into three birds one, two and ST right? Also this point as the coordinates minus 20. Well at this point as the coordinates cuomo Tzeitel. No Let us write the equations of 1st 2nd, 3rd part. The equation for the first part becomes why minus zero is equals to two minus zero. Dubai Dubai minus five minus minus two, multiplied by X- -2. Consol ving this be good. Why is equals to -2 divided by three. Multiplied by x plus two. The second part it is a part of a surgical with radios two So we have x square plus y squared is equal to two square which gives it Y is equal to minus square root four minus x squared. They're using minus sign as this part lies in negative quadrant for third. Do you have y minus zero is equals to do minus zero divided by him five minus two. Multiplied by x minus two. Which on simplification gives y will be equal to minus two divided by three, Multiplied by X -2. So combining these three we can write the function for f dash eggs as minus two by three. Two divided by three. Multiplied by x plus two. for expiring from -5, two minus two minus square root four minus x square. For exit wearing between -2 to do While -2 divided by three Multiplied by X -2 for exporting between two and for you this is a function of dash eggs so let us take the second. But do we have this dash eggs is equals two minus square root four minus x square for all x belongings. To close interval -2- two. Right? No integrating both the sides we'll have if for example is equals to minus integrating square root four minus X squared the eggs solving this million -1 x two, eggs square root four minus X squared mine is well I do signing words Eggs divided by two. Place constant of integration. No, here it is given that F equals to one, So substituting x equals to two and solving we'll get to see is equals to one plus fight, this is one value which should be noted, so we get to fx is equal to substituting the value of c miners, Eggs divided by two square root four minus x squared minus Do we signing words Eggs divided by two plus one, flirts fighting If X equals minus two and substituting this we'll get if minus two is equals to to buy plus one. Let us name this as equation one If mine is too No some equation let's name this is because we already have equations by the name of fun. So from equation one we have X equals f. Dash exit is equal to minus two divided by three X plus two X belongings too -5: -2. Right integrating good designs we get it's exciting is equal to -2 divided by three Integrating X-plus two dx which is equal to on integrating this we'll get to -2 divided by three, multiplied by X Square by two please. Two eggs Plus constant of integration say C1 again. And for the simplification we'll get minus X squared divided by three minus four eggs divided by three. Close C one. So here we have if minus two is equals to to pay plus one, solving for this we're getting C one Is equal to two pi minus one by three. Again this is something to be noted. Right? So using this weekend f x is equal soon minus X squared divided by three -4 x divided by three please two pi -1 x three so we have to find the value but if mine is fine Will be equals two minus minus five square Divided by three four, multiplied by -5 divided by three -1 divided by three. Which on solving goose To buy -2. This is a required solution. Thank you

Questions And Worked Solutions For AP Calculus BC Multiple Choice 2012

AP Calculus BC Multiple Choice 2012 Questions - complete paper (pdf)

AP Calculus BC 2012 MCQ Part B Solutions

AP Calculus BC Multiple Choice 2012 Question 1

1. If y = sin3x, then dy/dx =
   (A) cos3x (B) 3cos2x (C) 3sin2x (D) -3sin2xcos x (E) 3sin2x cos x

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AP Calculus BC Multiple Choice 2012 Question 2
2. The position of a particle moving in the xy-plane is given by the parametric equations x(t) = t32 and y(t) = 12t - 3t2. At which of the following points (x,y), is the particle at rest?
(A) (-4, 12) (B) (-3, 6) (C) (-2, 9) (D) (0, 0) (E) (3,4)

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AP Calculus BC Multiple Choice 2012 Question 3
3. The graph of f is shown above for 0 ≤ x ≤ 4. What is the value of ? (A) -1 (B) 0 (C) 2 (D) 6 (E) 12

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AP Calculus BC Multiple Choice 2012 Question 4
4. Which of the following integrals gives the length of the curve y = ln x from x = 1 to x = 2 ?

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AP Calculus BC Multiple Choice 2012 Question 5
5. The Maclaurin series for the function f is given by .What is the value of f(3) ?
(A) -3 (B) -3/7 (C) 4/7 (D) 13/16 (E) 4

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AP Calculus BC Multiple Choice 2012 Question 6
6. Using the substitution u = x2 -3, is equal to which of the following?

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AP Calculus BC Multiple Choice 2012 Question 7
7. If arcsin x = ln y then dy/dx =

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AP Calculus BC Multiple Choice 2012 Question 8
8. 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?
(A) 64.9 (B) 68.2 (C) 114.9 (D) 116.6 (E) 118.2

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AP Calculus BC Multiple Choice 2012 Question 9
9. Which of the following series converge?

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AP Calculus BC Multiple Choice 2012 Question 10

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AP Calculus BC Multiple Choice 2012 Question 11
11. Let f be the function defined by f(x) = √(|x-2|) for all x. Which of the following statements is true?
(A) f is continuous but not differentiable at x = 2.
(B) f is differentiable at x = 2.
(C) f is not continuous at x = 2.
(D) lim f(x) ≠ 0
(E) x = 2 is a vertical asymptote of the graph of f.

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AP Calculus BC Multiple Choice 2012 Question 12
12. The points (-1,-1) and (1,-5) are on the graph of a function y = f(x) that satisfies the differential equation dy/dx = x2 + y. Which of the following must be true?
(A) (1,-5) is a local maximum of f.
(B) (1,-5) is a point of inflection of the graph of f.
(C) (-1,-1) is a local maximum of f.
(D) (-1,-1) is a local minimum of f.
(E) (-1,-1) is a point of inflection of the graph of f.

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AP Calculus BC Multiple Choice 2012 Question 13
13. What is the radius of convergence of the series

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AP Calculus BC Multiple Choice 2012 Question 14
14. Let k be a positive constant. Which of the following is a logistic differential equation?

AP Calculus BC Multiple Choice 2012 Question 15
15. The graph of a differentiable function f is shown above. If h(x) = , which of the following is true?

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AP Calculus BC Multiple Choice 2012 Question 16
16. 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 ?

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AP Calculus BC Multiple Choice 2012 Question 17
17. For x > 0, the power series converges to which of the following?

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AP Calculus BC Multiple Choice 2012 Question 18
18. 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) =
(A) 2π - 2
(B) 2π - 3
(C) 2π - 5
(D) 6 - 2π
(E) 4 - 2π

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AP Calculus BC Multiple Choice 2012 Question 19
19. 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?
(A) (0,0) only
(B) (1/2, 1/5) only
(C) (0,0) and (-4,2)
(D) (0,0) and (4,2/3)
(E) There are no such points.

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AP Calculus BC Multiple Choice 2012 Question 20

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AP Calculus BC Multiple Choice 2012 Question 21
21. The line y = 5 is a horizontal asymptote to the graph of which of the following functions?

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AP Calculus BC Multiple Choice 2012 Question 22
22. The power series converges at x = 5. Which of the following must be true?

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AP Calculus BC Multiple Choice 2012 Question 23
23. 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?

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AP Calculus BC Multiple Choice 2012 Question 24
24. Let f be a differentiable function such that. Which of the following could be f(x) ?

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AP Calculus BC Multiple Choice 2012 Question 25

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AP Calculus BC Multiple Choice 2012 Question 26
26. What is the slope of the line tangent to the polar curve r = 1 + 2sinθ at θ = 0?

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AP Calculus BC Multiple Choice 2012 Question 27
27. For what values of p will both series converge?

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AP Calculus BC Multiple Choice 2012 Question 28
28. Let g be a continuously differentiable function with g(1) = 6 and g'(1) = 3.

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