The graph of the function f is made of the transforms of parts of the graphs of y=√x , y=1, y= 1/x
http://imageshack.us/photo/my-images/231…
lim x-> +∞ f(x) =
lim x-> -∞ f(x) =
lim x-> -1^+ f(x) =
lim x-> -1^- f(x) =
lim x-> 0^+ f(x) =
lim x-> 0^- f(x) =
thanks a bunch!
http://imageshack.us/photo/my-images/231…
lim x-> +∞ f(x) =
lim x-> -∞ f(x) =
lim x-> -1^+ f(x) =
lim x-> -1^- f(x) =
lim x-> 0^+ f(x) =
lim x-> 0^- f(x) =
thanks a bunch!
-
lim x-> +∞ f(x) = +∞
lim x-> -∞ f(x) = 0
lim x-> -1^+ f(x) = 1
lim x-> -1^- f(x) = -∞
lim x-> 0^+ f(x) = 1
lim x-> 0^- f(x) = 1
lim x-> -∞ f(x) = 0
lim x-> -1^+ f(x) = 1
lim x-> -1^- f(x) = -∞
lim x-> 0^+ f(x) = 1
lim x-> 0^- f(x) = 1
-
Just use the graph, as it goes to positive infinity, it is in the right area, and negative infinity is in the left area. As it approaches an area where the piece-wise function splits, there is only a limit if the lines on the graph connect, so the limit as x approaches -1 is non-exist ant.