Name: ______________________ Class: _________________ Date: _________ ID: A1Test 3 Review for FinalMultiple ChoiceIdentify the choice that best completes the statement or answers the question.1. A spherical party balloon is being inflated by helium pumped in at a rate 3 cubic feet per minute. How fast is the radius growing at the instant when the radius has reached 1 foot? The volume of a sphere of radius r is V =43πr3.a.0.14 feet per minuteb.0.76 feet per minutec.0.24 feet per minuted.0.72 feet per minutee.0.64 feet per minute2. The base of a 25-foot ladder is being pulled away from a wall at a rate of 12 feet per second. How fast is the top of the ladder sliding down the wall at the instance when the base of the ladder is 15 feet from the wall?a.16 ft/sb.3 ft/sc.9 ft/sd.48 ft/se.36 ft/s3. A cylindrical bucket is being filled with paint at a rate of 4 cm 3/min. How fast is the level rising when the bucket starts to overflow? The bucket has a height of 50 cm and a radius of 10 cm.a.0.315 cm/minb.0.164 cm/minc.0.768 cm/mind.0.013 cm/mine.0.617 cm/min4. The weekly sales in Honolulu Red Oranges is given by the following.q = 1,102 − 19pCalculate the price that gives a maximum weekly revenue.a.$58.00b.$29.00c.$31.00d.$30.00e.$14.505. The consumer demand curve for tissues is given byq = (92 − p)2where p is the price per case of tissues and q is the demand in weekly sales. Determine the elasticity of demand E when the price is set at $30.Round the answer to the nearest hundredth.a.0.01b.0.97c.0.48d.0.65e.1.94Name: ______________________ ID: A26. Evaluate the integral.∫ ( −ex+ x−6−18) dxa.ex+x-55+ Cb.−ex+x-55−x8+ Cc.−ex−x-55−x8+ Cd.ex−x-55−18+ Ce.−x −x-55−18+ C7. Evaluate the integral.∫x + 4x5dxa.13x3+1x4+ Cb.13x3−1x4+ Cc.−14x3−1x3+ Cd.−13x3+1x4+ Ce.−13x3−1x4+ C8. Find f(x) if f(6) = -5 and the tangent line at (x, f(x)) has slope 7 ex+ 8.a.f(x) = 7 ex+ 8x − 7 e6+ 53b.f(x) = 7 ex+ 8x − 7 e6− 53c.f(x) = 7 ex+ 8x + 7 e6+ 53d.f(x) = 7 ex+ 8x + 7 e6− 53e.f(x) = 7 ex− 8x − 7 e6+ 539. The marginal cost of producing the xth box of computer disks is 8 +x290,000 and the fixed cost is $150,000. Find the cost function C(x).a.C(x) = 8x +x3270,000− 150,000b.C(x) = −8x +x3270,000+ 150,000c.C(x) =x3270,000+ 150,000d.C(x) = 8x +x3270,000+ 150,000e.C(x) =x3270,000− 150,000Name: ______________________ ID: A310. Evaluate the integral.∫ (−5x + 4 )−2dxa.( − 5x2+ 4 )−15+ cb.( −5x + 4 )−15+ cc.( 5x + 4 )−35+ cd.( −5x + 4 )−110+ ce.( 5x + 4 )−310+ c11. Evaluate the integral.∫ xe−8x2+ 8dxa.−xe8x2+ 816+ cb.−e8x2+ 88+ cc.−e8x2+ 8+ cd.−16e8x2+ 8+ ce.−e8x2+ 816+ c12. Evaluate the integral.∫−2x − 6( x2+ 6x + 5 )3dxa.(x2+ 6x + 5)−2+ cb.(x2+ 6x + 5)−32+ cc.−1x2+ 6x + 5+ cd.(x2+ 6x + 5)−22+ ce.−(x2+ 6x + 5)−22+ c13. Evaluate the integral.∫ x( x − 3 )8dxa.(x − 3)1010−(x − 3)93+ cb.x(x − 3)10+ (x − 3)9+ cc.(x − 3)99−(x − 3)1010+ cd.(x − 3)1010+(x − 3)93+ ce.x(x − 3)99−(x − 3)1090+ cName: ______________________ ID: A414. Evaluate the integral.∫e−0.025x1 − e−0.025xdxa.−0.025 ln |1 − e−0.025x| + cb.0.025 ln |1 − e−0.025x| + cc.ln |1 − e−0.025x|40+ cd.−40 ln |1 − e−0.025x| + ce.40 ln |1 − e−0.025x| + c15. Find f(x) if f(0 ) = 0 and the tangent line at (x, f(x)) has the slope x(x2+ 4 )3.a.(x2+ 4)48− 32b.(x2+ 4)44− 64c.(x2+ 4)44+ 64d.x2+ 48e.x2+ 48+ c16. The velocity of a particle moving in a straight line is given by v = t( t2+ 5 )4+ 4t.Given that the distance s = 0 at t = 0, find an expression for s in terms of t without any unknown constants.a.s( t) =( t2+ 5)510+4t22+ 312.5b.s( t) =( t2+ 5)510+4t22c.s( t) =( t2+ 5)510+4t22− 312.5d.s( t) =( t2+ 5)52+4t22− 312.5e.s( t) =( t2+ 5)52+4t22+ 312.517. Calculate the left Riemann sum for the function over the given interval using the given values of n . f(x) = 6x − 2 over [0, 2] , n = 4a.Left Sum = 7b.Left Sum = - 4c.Left Sum = 4d.Left Sum = - 5e.Left Sum = 5Name: ______________________ ID: A518. Calculate the Riemann Sum for the integral using n = 10.12∫ 4xe1.4xdxRound the answer to four decimal places.a.51.5075b.64.6632c.515.0749d.63.0411e.63.852219. Evaluate the integral.25∫ (x3− 10x) dxa.11b.47c.200d.108e.15220. Evaluate the integral.49∫ 11exdxa.11 e10− e5ÊËÁÁÁÁÁÁˆ¯˜˜˜˜˜˜b.11 e9− e4ÊËÁÁÁÁÁÁˆ¯˜˜˜˜˜˜c.11 e8+ e3ÊËÁÁÁÁÁÁˆ¯˜˜˜˜˜˜d.11e5e.e9− e4ÊËÁÁÁÁÁÁˆ¯˜˜˜˜˜˜21. Evaluate the integral.36∫45x2x3− 12dxa.15 ( ln 204 - ln 15 )b.22.5 ( ln 204 + ln 15 )c.22.5 ( ln 204 - ln 15 )d.30 ( ln 204 + ln 15 )e.45 ( ln 15 - ln 204 )22. Evaluate the integral. ∫ (4x − 7) e−xdxa.(3 − 4x) e−x+ Cb.(3 + 4x) e−x+ Cc.(11 + 4x)e−x+ Cd.(11 − 4x) e−x+ Ce.(-3 + 4x) e−x+ CName: ______________________ ID: A623. Evaluate the integral. ∫ (x2+ 6) e3x + 6dxa.e3x + 627( 9x2− 6x + 56 ) + Cb.e3x + 63( 9x2+ 6x − 56 ) + Cc.e3x + 627( 9x2+ 6x − 56 ) + Cd.e3x + 69( 9x2− 6x + 56 ) + Ce.e3x + 627( 9x2− 6x − 56 ) + C24. Evaluate the integral. ∫ x2ln ( 2x)dxa.x3(3ln 2x + 1)9+ Cb.3x2ln 2x − x39+ Cc.3x2ln 2x − x9+ Cd.x3(3ln 2x − 1)9+ Ce.3x3ln 2x − x29+ C25. Evaluate the integral. 12∫ xln ( 3x) dxa.2 ln 6 −3 ln 32−94b.2 ln 6 −ln 32−34c.−ln 36 +ln 3 − 12d.ln 36 +ln 3 + 12e.3 ln 32−34ID: A1Test 3 Review for FinalAnswer SectionMULTIPLE CHOICE1. ANS: C PTS: 12. ANS: C PTS: 13. ANS: D PTS: 14. ANS: B PTS: 15. ANS: B PTS: 16. ANS: C PTS: 17. ANS: E PTS: 18. ANS: B PTS: 19. ANS: D PTS: 110. ANS: B PTS: 111. ANS: E PTS: 112. ANS: D PTS: 113. ANS: D PTS: 114. ANS: E PTS: 115. ANS: A PTS: 116. ANS: C PTS: 117. ANS: E PTS: 118. ANS: A PTS: 119. ANS: B PTS: 120. ANS: B PTS: 121. ANS: A PTS: 122. ANS: A PTS: 123. ANS: A PTS: 124. ANS: D PTS: 125. ANS: B PTS: