Fiesta 2
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AP CALCULUS AB| FALL 2008 | SHUBLEKA | FIESTA #2
Show all your work for full credit. Write your answers on a separate page. Problem 1 Consider f ( x) = x + − x . Find lim f ( x ) if it exists. Is the function continuous at 2? x→2
Problem 2 Show by means of an example that lim ( f + g ) may exist even though neither lim f nor lim g exists. x →a
x →a
x →a
Problem 3 Show by means of an example that lim ( fg ) may exist even though neither lim f nor lim g exists. x →a
Problem 4
(
)
Show that lim x 4 cos ( 1x ) = 0. x →0
Problem 5 Find the limit if it exists. If the limit does not exist, explain why.
lim ( 2 x + x − 3 ) x →3
+ 1x x →−4 4 + x lim
1 4
x →a
x →a
Show all your work for full credit. Write your answers on a separate page. Problem 1 Consider f ( x) = x + − x . Find lim f ( x ) if it exists. Is the function continuous at 2? x→2
Problem 2 Show by means of an example that lim ( f + g ) may exist even though neither lim f nor lim g exists. x →a
x →a
x →a
Problem 3 Show by means of an example that lim ( fg ) may exist even though neither lim f nor lim g exists. x →a
Problem 4
(
)
Show that lim x 4 cos ( 1x ) = 0. x →0
Problem 5 Find the limit if it exists. If the limit does not exist, explain why.
lim ( 2 x + x − 3 ) x →3
+ 1x x →−4 4 + x lim
1 4
x →a
x →a
