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ap calculus bc summer assignment 104 points this packet is a review of some precalculus topics and some calculus topics it is to be done neatly and on a separate ...

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                                      AP Calculus (BC) Summer Assignment (104 points) 
                   This packet is a review of some Precalculus topics and some Calculus topics. It is to be done 
                   NEATLY and on a SEPARATE sheet of paper.  Use your discretion as to whether you should 
                   use a calculator or not. When in doubt, think about if I would use one – that should guide you! 
                   Points will be awarded only if the correct work is shown, and that work leads to the correct 
                   answer. Have a great summer and I am looking forward to seeing you in September.  
              
              
                   Part I: First, let’s whet your appetite with a little Precalc! (12 points) 
                    
                   1)           For what value of k are the two lines                                                 and                                                                          
               2                                                                                   23xky
                                                                                                                               xy1
                                (a) parallel? (b) perpendicular? 
                    
               2  2)            Consider the circle of radius 5 centered at (0, 0).  Find an equation of the line tangent to 
                                the circle at the point (3, 4) in slope intercept form. 
                    
               3  3)            Graph the function shown below. Also indicate any key points and state the domain and 
                                range. 
                    
                                                       2
                                            4,x
                                                                x 1
                                            33
                                            
                                 f (x) x                 ,
                                                                13x
                                                                                                                                                 
                                            22
                                            x3,               x 3
                                            
                                            
                    
               2  4)            Write a piecewise formula for the function shown. Include the domain of each piece! 
                    
                                             
                    
                    
                                                                    
                    
                    
                    
                    
                                                                    
                    
                    
                    
                    
                                                                                                                                          
                    
                    
                    
                                                                   
                    
                    
                      5)            Graph the function                                   x         and indicate asymptote(s). State its domain, range, and 
               3                                                             ye32
                                    intercepts. 
                       
                       
                      Part II: Unlimited and Continuous! (11 points) 
                       
                      For #1-2 below, find the limits, if they exist.(#1-8 are 1 pt each) 
                              
                                                 32                                                                                               x 3
                                            2x 7x               4x                                                                   lim
                             1)  lim                                                                                    2)                                                       
                                     x4              x4                                                                              x9      9x
                              
                              
                      For #3-4, explain why each function is discontinuous and determine if the discontinuity is removable or 
                      nonremovable. 
                       
                                                    2xx3,              3                                                                         2
                                     gx()                                                                                                      xx10             25
                             3)                                                                                         4)   hx()                                         
                                                  xx5,             3                                                                               x5
                                                  
                       
                       
                      For #5-8, determine if the following limits exist, based on the graph below of p(x).  If the limits exist, state 
                      their value.  Note that x = -3 and x = 1 are vertical asymptotes. 
                              
                                                                                                                          y
                              
                                                                                                                    
                              
                                                                                                                    
                              
                                                                                                                    
                              
                                                                                                                    
                                                                                                                                                                              x
                              
                                                                                                                                     
                                                                                                                   
                              
                                                                                                                   
                              
                                                                                                                   
                              
                                                                                                                   
                              
                                                                                                                   
                                    5)             lim px( )                                6)              lim px( )                               7)             lim px( )                   
                                                                                                                                                                 x3
                                                   x1                                                     x3
                              
                                    8)             lim px( ) 
                                                   x1
                              
                                                                                                                       2 
                                                                     2
                                                                 x kx               x  5
                3  9)       Consider the function  f (x)                                  ,  
                                                                         
                                                                   5sin     x       x  5
                                                                              
                                                                         2
                                                                              
                                                                 
                            In order for the function to be continuous at x = 5, the value of k must be 
               
               
               
              Part III: Designated Deriving! (20 points) 
               
                        lim       sec( h)sec() 
          1   1)                             h               
                        h0
               
               
               
              For #2-5, find the derivative.  
               
          2   2)        y  ln(1ex)                                      2    3)        y  csc(1      x) 
               
               
          2   4)        y  7 x3 4x2                                     3    5)        f (x) (x 1)e3x                                        
               
               
          2   6)        Consider the function  f (x)             x2.  On what intervals are the hypotheses of the Mean 
                        Value Theorem satisfied? 
               
               
                              2     3      2              dy
          2   7)        If  xy  y x 5, then dx  
               
               
          2   8)        The distance of a particle from its initial position is given by s(t)  t 5                        9    , where s 
                                                                                                                          (t 1)
                        is feet and t is minutes.  Find the velocity at t = 1 minute in appropriate units. 
               
               
              Use the table below for #9-10. 
               
                                                                                           
                                                  X     f (x)    g(x)      f (x)     g( x)
                                                  1      4         2         5         ½ 
                                                  3       7       -4         3         -1 
                                                                             2
               
                                          d                                                                         d  f 
           1  9)        The value of         ( f  g)  at x = 3 is                  1   10)      The value of                at x = 1 is 
                                          dx                                                                        dx g 
                                                                                                                           
               
               
                                                                              3 
                  In #11-12, use the table below to find the value of the first derivative of the given 
                  functions for the given value of x. 
                   
                     x                                                       
                               f (x)        g(x)         f (x)        g( x)
                     1           3            2            0             3  
                                                                         4
                     2           7           -4            1            -1 
                                                           3
                   
                   
              1   11)                    2 at x = 2 is                                                      1    12)          f (g(x))at x = 1 is 
                              [ f (x)]
                   
                   
                   
                  Part IV: Derived and Applied! (15 points) 
                   
                  For #1-3, find all critical values, intervals of increasing and decreasing, any 
                  local extrema, points of inflection, and all intervals where the graph is concave 
                  up and concave down. 
                   
                                           x2 5
              4   1)           fx() x4  
                   
              3   2)           y 3x3 2x2 6x2  
                               
              1   3)          The graph of the function  y  x5  x2 sinx changes concavity at x =  
                   
             1                                                                                                                    7     3
                                                                                                                          yx
                  4)          For what value of x is the slope of the tangent line to                                                   x  undefined? 
                   
                   
                  5)                       
                                                                           Y                    
                   
                   
                   
                                                                         O               X 
                   
                              A ladder 15 feet long is leaning against a building so that end X is on level ground and 
                              end Y is on the wall as shown in the figure.  X is moved away from the building at a 
                              constant rate of ½ foot per second. 
                                   
                                3   (a)         Find the rate in feet per second at which the length OY is changing when X is 
                                                9 feet from the building. 
                                3   (b)         Find the rate of change in square feet per second of the area of triangle XOY 
                                                when X is 9 feet from the building. 
                   
                   
                                                                                                    4 
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...Ap calculus bc summer assignment points this packet is a review of some precalculus topics and it to be done neatly on separate sheet paper use your discretion as whether you should calculator or not when in doubt think about if i would one that guide will awarded only the correct work shown leads answer have great am looking forward seeing september part first let s whet appetite with little precalc for what value k are two lines xky xy parallel b perpendicular consider circle radius centered at find an equation line tangent point slope intercept form graph function below also indicate any key state domain range x f write piecewise formula include each piece asymptote its ye intercepts ii unlimited continuous limits they exist pt lim explain why discontinuous determine discontinuity removable nonremovable xx gx hx following based p their note vertical asymptotes y px kx sin order must iii designated deriving sec h...

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