AP Calculus AB Exam Review Limits and Continuity …

1 AP Calculus AB Exam ReviewLimits and ContinuityMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the the )Assume that a watermelon dropped from a tall building falls y = 16t2 ft in t sec. Find thewatermelon's average speed during the first 6 sec of )97 ft/secB)48 ft/secC)96 ft/secD)192 ft/sec1)Determine the limit by )limx 4 x2 + 14x + 49A)121B)Does not existC) 11D)112)Determine the limit algebraically, if it )limx 0 x3 + 12x2 5x5xA)0B)Does not existC) 1D)53)Determine the limit graphically, if it )limx 1 f(x)x-5-4 -3 -2 -11 2 3 4 5f(x)54321-1-2-3-4-5x-5-4 -3 -2 -11 2 3 4 5f(x)54321-1-2-3-4-5A)Does not existB)12C) 1D)24)Find the indicated )limx 3 int xA) 3B) 4C)4D)05)

2 1 Match the function with the correct table )f(x) = x2 2x 8x2 9x + 20 x (x)A) ; ; ; ; ; ) ; ; ; ; ; ) ; ; ; ; ; ) ; ; ; ; ; )Find the )Let limx 1f(x) = 49. Find limx 1f(x).A) 1B)7C) )497)Evaluate or determine that the limit does not exist for each of the Limits (a) limx d f(x), (b) limx d+ f(x), and (c) limx d f(x)for the given function f and number ) f(x) = x2 4, for x < 0, 3,for x 0d = 4A)(a) 4(b) 3(c) Does not existB)(a) 12(b) 12(c) 12C)(a) 4(b) 3(c) 3D)(a) 3(b) 4(c) Does not exist8)Provide an appropriate )It can be shown that the inequalities x x cos(1x) xhold for all values of x 0.

3 Find limx 0x cos(1x) if it existsA)Does not existB) )1D)09)Find the limit, if it )limx cos 3xxA)0B) C)3D)110)2 Find the indicated )limx sin xxA)1B) C)0D)Does not exist11)Find the )limx 0+(1 + csc x )A) B)1C)0D) 12)Find the vertical asymptotes of the graph of f(x).13)f(x) = sec xA)x = 2 + n , n is any integerB)x = 0C)x = n , n is any integerD)x = 13)3 Match the function with the graph of its end behavior )y = 2x3 5x2+ 1x + 9A)x-40-2020 40y400200-200-400x-40-2020 40y400200-200-400B)x-40-2020 40y400200-200-400x-40-2020 40y400200-200-400C)x-40-2020 40y400200-200-400x-40-2020 40y400200-200-400D)x-40-2020 40y400200-200-400x-40-2020 40y400200-200-40014)Find a power function end behavior )y = 4x2 2x + 7A)y = 4x2B)y = 4x2 + 7C)y = 4x2 2xD)y = 4x 215)

4 Find a simple basic function as a right end behavior model and a simple basic function as a left end behavior )y = 4x + lnxA)y = 4x; y = 4xB)y = 4x; y = 4xC)y = 4x; y = ln xD)y = x; y = ln x16)Find the limit, if it )limx x4exA)0B)4C)1D) 17)4 Find the limit of f(x) as (a) x , (b) x , (c) x 0 , and (d) x 0+.18)f(x) = x 4x 2, x 01x2,x > 0A)(a) (b) (c) 4(d) 2B)(a) 1(b) 0(c) 2(d) C)(a) 2(b) Does not exist(c) 1(d) 0D)(a) (b) 2(c) 0(d) 118)Find the intervals on which the function is )y = 49x 8A) 89, B) , 89C)89, D)89, 19)Find the points of discontinuity.

5 Identify each type of )y = x + 4x2 14x + 48A)x = 6, x = 8, both infinite discontinuitiesB)x = 6, infinite discontinuityC)x = 6, x = 8, both infinite discontinuitiesD)x = 8, infinite discontinuity20)Find all points where the function is )A)x = 4B)NoneC)x = 2D)x = 4, x = 221)Give a formula for the extended function that is continuous at the given )f(x) = sin 5xx, x = 0A)y = sin 5xx, x 05,x = 0B)y = sin 5xx, x = 05,x 0C)y = 5xD)y = sin 5x22)5 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the an appropriate )Verify that the function f(x) = 4x2 + xx is continuous.

6 Indicate which theorems are neededand which functions are assumed to be continuous for all x in the )MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the a value for a so that the function f(x) is )f(x) = x2 5, x < 45ax, x 4A)a = 9B)a = 11C)a = 1120D)a = 4524)Solve the )Consider the learning curve defined in the graph. Depicted is the accuracy, p, expressed as apercentage, in performing a series of short tasks versus the accumulated amount of time spentpracticing the tasks, t.

7 Is p(t) continuous at t = 25? at t = 40? at t = 45?A)Yes; no; noB)No; no; noC)Yes; no; yesD)Yes; yes; yes25)6 Answer KeyTestname: Limits AND CONTINUITY1)C2)D3)C4)D5)B6)D7)B8)B9)D10) A11)C12)D13)A14)D15)A16)B17)A18)B19)C20) A21)A22)A23)Assume y = x and the square root function are continuous. Use the sum, constant multiple, product, and quotienttheorems of )C25)C7