ࡱ>  npmCDEFG bjbjVV <<d/||wwwG<:I8"""HHHHHHH$2JL\Hw""@"""HH'''"4<wH'"H''RD|GH 2#EH I0:IEb0M$0M<G0MwG""'"""""HHj&$""":I""""0M"""""""""| : AP Calculus AB Fall Final Exam Review 1) Find the limit.  EMBED Equation.3  2) Find the limit of the function: f(x) =  EMBED Equation.3  as x approaches  EMBED Equation.3 . 3) Evaluate:  EMBED Equation.3  4) Evaluate:  EMBED Equation.3  5) Find the limit:  EMBED Equation.3  6) Find the limit:  EMBED Equation.3  7) Let  EMBED Equation.3 . Find the limit:  EMBED Equation.3 . 8) Find the limit:  EMBED Equation.3 . 9) Find the horizontal asymptote(s) of  EMBED Equation.3  10) Find the value(s) of x at which the curve  EMBED Equation.3  has a vertical asymptote. 11) Find the limit:  EMBED Equation.3  12) Find the limit:  EMBED Equation.3  13) Find the value(s) of x at which the function f(x) =  EMBED Equation.3  is discontinuous. 14) For what value of the constant c is the function f continuous on  EMBED Equation.3 ?  EMBED Equation.3  15) At what value(s) of x is the function  EMBED Equation.3  discontinuous? 16) Let  EMBED Equation.3  and  EMBED Equation.3 . Find  EMBED Equation.3 . 17) Find  EMBED Equation.3 . 18) Let EMBED Equation.3 . If f(x) is differentiable at x = 2, what is the value of a? 19) For the curve f(x) = EMBED Equation.3 , find the slope of the secant line through the points (4, f(4)), and (25, f(25)). 20) Find the slope of the tangent to  EMBED Equation.3  at x = 4. 21) Find the equation of the line tangent to  EMBED Equation.3  at x = 2. 22) If f(x) =  EMBED Equation.3 , find the slope of the line tangent to f(x) at the point ((1, 36). 23) Find the slope of the line tangent to the curve  EMBED Equation.3  at the point (1, 4). 24) For the curve EMBED Equation.3 , find the slope of the tangent line at the point where x = 1. 25) Find an equation of the tangent line to  EMBED Equation.3  at the point where x = 3. 26) If the tangent line to y = f (x) at (5, 1) also passes through the point (2, 7), then f '(5) = _______? 27) Given the graph of the derivative, sketch the original function on the same axes: 28) Estimate all value(s) of x (if any) that satisfy the Mean Value Theorem for the function  EMBED Equation.3 . 29) If y =  EMBED Equation.3 , then  EMBED Equation.3 = 30) Find the acceleration at t = 2 given s(t) =  EMBED Equation.3 . 31) Find the derivative of  EMBED Equation.3  32) Find the interval where the function is concave down:  EMBED Equation.3  33) A box with a square base and open top must have a volume of 32,000  EMBED Equation.3 . Find the dimensions of the box which will minimize the amount of material used. 34) Given the graph of  EMBED Equation.3  below, at which point is it true that  EMBED Equation.3   35) Find the critical number c for  EMBED Equation.3  at which f(c) is not a local maximum and not a local minimum. 36) Find the xcoordinate of the point of inflection of the function  EMBED Equation.3  37) Given that  EMBED Equation.3  has a relative maximum at x = 6, choose the correct statement. A)  EMBED Equation.3  is positive on the interval  EMBED Equation.3 . B)  EMBED Equation.3  is negative on the interval  EMBED Equation.3 . C)  EMBED Equation.3  is positive on the interval  EMBED Equation.3 . D)  EMBED Equation.3  is negative on the interval  EMBED Equation.3 . 38) Given that EMBED Equation.3  has critical numbers at x =1 and x = 3, find a and b. 39) The equation of motion is given for a particle, where s is in meters and t is in seconds. Find the acceleration after 4.5 seconds.  EMBED Equation.3  40) A particles position is given by  EMBED Equation.3  for  EMBED Equation.3 . When is the particle at rest? 41) Find the minimum value of  EMBED Equation.3  on  EMBED Equation.3 . 42) What is the slope of the tangent line to  EMBED Equation.3  at  EMBED Equation.3 ? 43) Two positive numbers, a and b, multiply to 18. If we wish to minimize 2a + b, what must the value of a be? 44) Find the point(s) of inflection, if any, of  EMBED Equation.3 . 45) If h(x) = f(g(x)), g(3) = 6, g(3) = (8,  EMBED Equation.3 (3) = 2 and  EMBED Equation.3 (6) = 8, find  EMBED Equation.3 (3). 46) If y = EMBED Equation.3 , calculate  EMBED Equation.3 . 47) Find the derivative of y =  EMBED Equation.3 . 48) Find  EMBED Equation.3 :  EMBED Equation.3 . 49) Let  EMBED Equation.3  and  EMBED Equation.3 . Find the value of  EMBED Equation.3  when x = 1. 50) Find the derivative:  EMBED Equation.3  51) What is EMBED Equation.3 ? y = cos(5x) 52) Find  EMBED Equation.3 .  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