Fiesta 4: Ap Calculus Ab | Limits And Continuity | 2009-2010

AP Calculus AB | Fiesta 4 | Limits and Continuity | Shubleka  

NAME __________________ Write your solutions neatly on separate sheets. No graphing calculators are allowed.

1. Find the limit: a.

2− x 2 x →1 ( x −1)

b. lim

lim x csc x

x → 2π −

2. Sketch the graph of an example of a function f that satisfies all of the given conditions: lim+ f ( x) = 4 , lim− f ( x) = 2 , lim f ( x ) = 2 , f (3) = 3 , f (−2) = 1 x →3

x →−2

x →3

3. Is there a number a such that:

lim 3 x x+2 +axx+−a2+3 exists? If so, find the value of a and the value of 2

x →−2

the limit. 4. If

lim ( f + g ) = 2 and lim ( f − g ) = 1 , find lim ( fg ) . x →a x →a

x →a

5. Discuss the function f ( x) = a x b + a − x b in as much detail as possible: sketch a graph, describe its domain, then discuss limits and continuity.