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

Transcription

1 Eam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine from the graph whether the function has an absolute etreme values on the interval [a, b]. ) A) Absolute minimum and absolute maimum. B) Absolute maimum onl. C) No absolute etrema. D) Absolute minimum onl. ) Determine all critical points for the function. ) = - 6 A) = 0 and = B) = C) = 0 D) = 0, =, and = - ) Find the absolute etreme values of the function on the interval. ) g() = 7 -, - A) absolute maimum is at = 0; absolute minimum is -8 at = - B) absolute maimum is at = 0; absolute minimum is -8 at = C) absolute maimum is at = 0; absolute minimum is - at = D) absolute maimum is 7 at = 0; absolute minimum is -8 at = ) ) h() = +, - ) A) absolute maimum is 7 at = ; absolute minimum is at = - B) absolute maimum is - at = -; absolute minimum is - at = C) absolute maimum is - at = ; absolute minimum is at = - D) absolute maimum is - at = -; absolute minimum is at =

2 Find the absolute etreme values of the function on the interval. ) f() = e -, - A) absolute minimum value is at = 0; absolute maimum value is e - at = B) absolute minimum value is e- + at = -; absolute maimum value is e - at = C) absolute minimum value is at = 0; absolute maimum value is e- + at = - D) absolute minimum value is at = 0; no maimum value ) 6) f() = ln( + ) +, 6) A) absolute minimum value is ln + at = ; absolute maimum value is ln 7 + at = B) absolute minimum value is - at = -; absolute maimum value is ln 7 + at = C) absolute minimum value is ln + at = ; absolute maimum value is ln 7 + at = D) absolute minimum value is ln + at = ; absolute maimum value is ln + at = Find the etreme values of the function and where the occur. 7) = + A) Absolute minimum value is 0 at = 0. B) Absolute maimum value is 0 at = 0. 7) C) Absolute minimum value is - at = -. Absolute maimum value is at =. D) Absolute minimum value is 0 at =. Absolute maimum value is 0 at = -. 8) = ( - ) / A) Absolute maimum value is 0 at = -. B) Absolute minimum value is 0 at =. C) Absolute minimum value is 0 at = -. D) There are no definable etrema. 8)

3 Solve the problem. 9) Select an appropriate graph of a twice-differentiable function = f() that passes through the points (-,), - 6, 9, (0,0), 6, 9 following sign patterns. and (,), and whose first two derivatives have the 9) : : A) 6 8 B) C) D)

4 0) The graph below shows the first derivative of a function = f(). Select a possible graph f that passes through the point P. 0) f P A) B) C) D)

5 ) The graphs below show the first and second derivatives of a function = f(). Select a possible graph f that passes through the point P. ) f f P P A) B) C) D) Find the largest open interval where the function is changing as requested. ) Decreasing f() = - A) -, B) -, ) C) -, - D),

6 Use the graph of the function f() to locate the local etrema and identif the intervals where the function is concave up and concave down. ) ) A) Local minimum at = ; local maimum at = 0; concave up on (0, ); concave down on (-, 0) B) Local minimum at = 0; local maimum at = ; concave down on (0, ); concave up on (-, 0) C) Local minimum at = ; local maimum at = 0; concave down on (0, ); concave up on (-, 0) D) Local minimum at = 0; local maimum at = ; concave up on (0, ); concave down on (-, 0) Sketch the graph and show all local etrema and inflection points. ) = ln (6 - ) )

7 A) No etrema No inflection point B) Local minimum (0, ln 6) No inflection point C) Local maimum (0, ln 6) No inflection point D) Local minimum (0, -ln 6) No inflection point For the given epression, find '' and sketch the general shape of the graph of = f(). ) = -/( - 6) ) 7

8 A) B) C) D) Solve the problem. 6) A long strip of sheet metal inches wide is to be made into a small trough b turning up two sides at right angles to the base. If the trough is to have maimum capacit, how man inches should be turned up on each side? A) in. on one side, in. on the other B) 6 in. C) in. D) in. 6) 8

9 7) The 9 ft wall shown here stands 0 feet from the building. Find the length of the shortest straight beam that will reach to the side of the building from the ground outside the wall. 7) 9' wall 0' A). ft B). ft C). ft D) 9 ft 8) Suppose a business can sell gadgets for p = dollars apiece, and it costs the business c() = dollars to produce the gadgets. Determine the production level and cost per gadget required to maimize profit. A) gadgets at $8.89 each B) 0,000 gadgets at $0.00 each C),0 gadgets at $7.0 each D),70 gadgets at $.0 each 8) Use l'hopital's Rule to evaluate the limit. 9) lim cos - 0 A) B) - C) 0 D) 9) Find the limit. 0) lim (ln ) / 0) A) 0 B) C) e D) Use l'hopital's Rule to evaluate the limit. ) lim + - ) A) B) 0 C) D) - 9

10 L'Hopital's rule does not help with the given limit. Find the limit some other wa. ) lim sec 0 csc A) B) - C) 0 D) ) Find an antiderivative of the given function. ) 8 cos 9 A) 8 sin 9 B) sin 9 C) - 7 sin 9 D) 8 9 sin 9 ) Find the most general antiderivative. ) sec θ dθ sec θ - cos θ ) A) -cot θ + C B) cos θ + C C) cot θ + C D) θ + tan θ + C ) 9-8 d + ) A) 9 tan- - ln + C B) 9 tan- + 8 ln + C C) 9 tan- - 8 ln + C D) tan ln 8 + C Solve the initial value problem. 6) d d = 7; (0) = -, (0) = 6, (0) = 6) A) = B) = C) = D) =

11 Which of the graphs shows the solution of the given initial value problem? 7) d = -, = 0 when = d 7) A) B) (, 0) (, 0) C) D) (, 0) (, 0) Solve the problem. 8) An object is dropped from ft above the surface of the moon. How long will it take the object to hit the surface of the moon if d s/dt = -. ft/sec? A). sec B). sec C). sec D).6 sec 8)

12 Graph the function f() over the given interval. Partition the interval into subintervals of equal length. Then add to our sketch the rectangles associated with the Riemann sum f(ck) Δk, using the indicated point in the kth k= subinterval for ck. 9) f() = cos +, [0, ], right-hand endpoint 9) A) B) C) D) Use a finite approimation to estimate the area under the graph of the given function on the stated interval as instructed. 0) f() = between = and = using the midpoint sum with four rectangles of equal width. A) B) 69 C) D) 0 0)

13 Graph the integrand and use geometr to evaluate the integral. 6 ) 6 - d -6 A) 6 B) 6 C) 8 D) 6 ) Solve the problem. 6 6 ) Suppose that f is continuous and that f(z) dz = 0 and f(z) dz =. Find - f() d. - - A) - B) - C) - D) ) Find the area of the shaded region. ) ) (/, ) (/, ) = = csc A) + B) - C) D) Evaluate the integral. ln ) e d 0 A) 8 B) C) D) 6 ) Find the total area of the region between the curve and the -ais. ) = ( + ) ; 6 A) 886 B) 7 C) 87 D) 9 ) Find the derivative. tan 6) = 0 t dt A) sec tan B) tan/ C) sec tan / D) tan 6)

14 Find the average value of the function over the given interval. 7) = - ; [-, ] 7) A) - B) 0 C) D) Evaluate the integral using the given substitution. 8) d, u = ) A) C B) 7 C) 7(7 + ) / + C D) 7 + C C Evaluate the integral. 9) t sin t + dt A) cos t + + C B) -cos t + + C C) cos t + + C D) - cos t + + C 9) 0) e d - e 0) A) sec- (e ) + C B) sin- (e ) + C C) - - e + C D) e sin- (e ) + C Use the substitution formula to evaluate the integral. / ) cos 0 ( + sin ) d A) 76 B) 88 C) - 6 D) - 88 ) ) 0 ln / e d + e 8 ) A) - B) C) 6 D) - 6

15 Solve the problem. ) Given the acceleration, initial velocit, and initial position of a bod moving along a coordinate line at time t, find the bod's position at time t. a = cos t, v(0) = -7, s(0) = - A) s = - 8 sin t - 7t - B) s = - 8 cos t - 7t - C) s = 8 sin t - 7t - D) s = 8 cos t + 7t - ) Find the area of the shaded region. ) = sec ) = cos A) - B) C) - D) + Find the area enclosed b the given curves. ) Find the area of the region in the first quadrant bounded b the line = 8, the line =, the curve =, and the -ais. ) A) B) C) D) 6 Find the volume of the solid generated b revolving the shaded region about the given ais. 6) About the -ais 6) = sin A) 9-9 B) 9 - C) D) 9

16 Find the volume of the solid generated b revolving the region bounded b the given lines and curves about the -ais. 7) =, = 0, =, = 9 7) A) 9 B) (ln 9) C) (ln 9) D) Find the length of the curve. 8) = 0 sin t - dt, 0 A) B) C) D) 8) Evaluate the integral. 9) sec tan d + sec A) ln sec + C B) ln + sec + C C) -ln + sec + C D) ln + sec + C 9) Find the derivative of with respect to, t, or θ, as appropriate. 0) = ln(cos(ln θ)) A) - tan(ln θ) θ B) tan(ln θ) C) -tan(ln θ) D) tan(ln θ) θ 0) Evaluate the integral. ) 0 ln e sin e d ) A) + cos B) C) - cos D) - ) (-) ln() d ) A) - ln C B) - ln C C) - ln C D) - ln C ) ln d A) 8. B). C) -.9 D). ) 6

17 ) 0 /8 sin 8 d ) A) 6 B) 0 C) D) 8 Evaluate the improper integral or state that it is divergent. ) d.66 A) B) Divergent C) D).66 ) 6) e 0e- d - A) 0 B) 0 C) Divergent D) -0 6) 7

18 Answer Ke Testname: PRACTICE FINAL ) C ) A ) D ) A ) A 6) A 7) C 8) B 9) D 0) A ) A ) A ) A ) C ) C 6) C 7) C 8) C 9) B 0) D ) C ) C ) D ) A ) C 6) D 7) D 8) A 9) D 0) A ) C ) C ) B ) C ) A 6) A 7) C 8) D 9) C 0) B ) A ) B ) B ) C ) C 6) A 7) C 8) D 9) B 8

19 Answer Ke Testname: PRACTICE FINAL 0) A ) A ) D ) B ) A ) D 6) C 9