MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Eam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the graph to evaluate the limit. ) lim 0 f() ) A) - B) 0 C)does not eist D) Find all points where the function is discontinuous. ) ) A) = 0 B) = -, = 0, = C) = -, = D) None Find the limit. ) lim - + ) A) - B) does not eist C) D) 0 Find the average rate of change of the function over the given interval. ) =, 0, 7 ) A) B) - 0 C) D) 7

2 Find the limit. ) lim A) 9 B) - 9 C) -9 D) 9 ) Provide an appropriate response. 6) Is f continuous at f()? 6) f() = - +,, -, - + 6, - < 0 0 < < = < < < < 6 d (, -) t A) Yes B) No Find the limit. 7) lim π/ 9 + sin(π sec ) 7) A) 0 B) C) 9 + D) 9

3 The graph of a function is given. Choose the answer that represents the graph of its derivative. 8) 8) A) B) C) D) Find the derivative of the function. 9) r = θ - 9 θ + 9 A) r = C)r = - 9 θ(θ + 9) 9 θ(θ + 9) 8 B) r = (θ + 9) θ - 8 D) r = 9 θ + 9 9)

4 Find d for the given function. d 0) = cot 0 A) - 0 csc C)6 csc 0 0 cot 0 B) -6 csc D) 0 csc 0 0 cot 0 0) Find. ) = + - ) A) - - B) C) D) 8 + Find the value(s) of for which the slope of the curve = f() is 0. 8 ) f() = + ) A) = 8 B) = 0 C) = -8 D) = - 8 Suppose u and v are differentiable functions of. Use the given values of the functions and their derivatives to find the value of the indicated derivative. ) u() =, u () = -6, v() = 7, v () = -. ) d (u- v) at = d A) 6 B) 0 C) -0 D) - Find the derivative of the function. ) r = (sec θ + tan θ)- A) -(sec θ tan θ + secθ) - B) -(sec θ + tan θ)- ) C) -(sec θ + tan θ)-(tan θ + sec θ tan θ) D) - sec θ (sec θ + tan θ) Find the etreme values of the function and where the occur. ) f() = - + A) Local maimum at (0, 0). B) None C)Local maimum at (, -), local minimum at (-, 8). D) Local maimum at (-, 8), local minimum at (, -). )

5 Provide an appropriate response. 6) Suppose the velocit of a bod moving along the s-ais is ds = 9.8t - 8. dt Is it necessar to know the initial position of the bod to find the bod's displacement over some time interval? Justif our answer. A) No, displacement has nothing to do with the position of the bod. B) Yes, integration is not possible without knowing the initial position. C)No, the initial position is necessar to find the curve s= f(t) but not necessar to find the displacement. The initial position determines the integration constant. When finding the displacement the integration constant is subtracted out. D) Yes, knowing the initial position is the onl wa to find the eact positions at the beginning and end of the time interval. Those positions are needed to find the displacement. 6) Find the largest open interval where the function is changing as requested. 7) Increasing = ( - 9) A) (, ) B) (-, 0) C)(-, 0) D) (-, ) 7) Solve the problem. 8) A private shipping compan will accept a bo for domestic shipment onl if the sum of its length and girth (distance around) does not eceed 0 in. What dimensions will give a bo with a square end the largest possible volume? 8) A) 0 in. 0 in. 00 in. B) 0 in. 0 in. 0 in. C)0 in. 0 in. 0 in. D) 0 in. 0 in. 0 in. 9) At noon, ship A was nautical miles due north of ship B. Ship A was sailing south at knots (nautical miles per hour; a nautical mile is 000 ards) and continued to do so all da. Ship B was sailing east at 6 knots and continued to do so all da. The visibilit was nautical miles. Did the ships ever sight each other? A) No. The closest the ever got to each other was 6. nautical miles. B) No. The closest the ever got to each other was. nautical miles. C)Yes. The were within nautical miles of each other. D) Yes. The were within nautical miles of each other. 9)

6 Provide an appropriate response. 0) Find the standard equation for the position s of a bod moving with a constant acceleration a along a coordinate line. The following properties are known: i. d s dt = a, ii. ds dt = v 0 when t = 0, and iii. s = s0 when t = 0, where t is time, s0 is the initial position, and v0 is the initial velocit. A) s = at + v0t + s0 B) s = at - v 0t - s0 C)s = at + s 0 D) s = at + v 0t + s0 0) Find the etreme values of the function and where the occur. ) f() = ( - )/ A) Absolute minimum value is 0 at =. B) Absolute maimum value is 0 at = -. C)There are no definable etrema. D) Absolute minimum value is 0 at = -. ) Find the most general antiderivative. ) ( t - t) dt ) A) t / - t / + C B) t - t + C C) t / - t / + C D) - t / - t -/ + C ) d ) A) / C B) / C C) - 6 +C D) / C Find the area of the shaded region. ) ) A) B) C) D) 6

7 Evaluate the integral b using substitution. cos sin ) d 8 ) A) sin / 76 + C B) sin / 76 + C C) sin / + C D) sin 8 + C Use a finite approimation to estimate the area under the graph of the given function on the stated interval as instructed. 6) f() = between = and = 6 using a left sum with four rectangles of equal width. A) 86 B) C)69 D) 6 6) Epress the sum in sigma notation. 7) A) k + B) k = k C) k = 0 (-)k k D) k = - k = 0 k + 7) Evaluate the integral. 8) sin (6 - ) d A) cos (6 - ) + C B) -cos(6 - ) + C 6 8) C) - 6 cos (6 - ) + C D) 6 cos (6 - ) + C Find the average value of the function over the given interval. 9) f() = + on [-7, 7] A) 8 B) 96 C)7 D) 9) Evaluate the integral. t + 0) dt t A) 9 B) 7 C) D) 77 0) Solve the problem. ) Suppose that f and g are continuous and that f() d = - and g() d = Find f() - g() d. 7 A) -6 B) - C) D) - ) 7

8 Estimate the value of the quantit. ) The table shows the velocit of a remote controlled race car moving along a dirt path for 8 seconds. Estimate the distance traveled b the car using 8 subintervals of length with left-end point values. ) Time Velocit (sec) (in./sec) A) 9 in. B) 9 in. C)98 in. D) in. Epress the sum in sigma notation. ) A) (k + ) B) k = 6 k C) k = (k - ) D) k = k = 0 (k + ) ) Find the volume of the solid generated b revolving the region bounded b the given lines and curves about the -ais. ) = 7, = 7, = 0 A) 98π B) π C) π D) π ) Find the volume of the solid generated b revolving the region about the given ais. Use the shell or washer method. ) The region in the first quadrant bounded b = - and the -ais about the -ais A) 0 8 π B) π C) π D) π ) Find the area enclosed b the given curves. 6) = sin, = csc, π π 6) A) - B) - C) - D) + 7) =, = ) A) B) 6 C) D) 8 8

9 Solve the problem. 8) A water tank is formed b revolving the curve = about the -ais. Find the volume of water in the tank as a function of the water depth,. A) V() = π / B) V() = π / C)V() = π / D) V() = π 9 9 8) 9

10 Answer Ke Testname: 70 FINAL REVIEW ) C ) A ) C ) D ) A 6) B 7) D 8) B 9) A 0) D ) C ) B ) B ) D ) D 6) C 7) A 8) B 9) B 0) D ) A ) C ) A ) A ) B 6) B 7) D 8) C 9) D 0) B ) D ) A ) D ) B ) B 6) C 7) B 8) A 0