14.2. Graphs to Find Limits http://www.ck12.org
Both of these limits exist because the left hand and right hand neighborhoods of these points seem to approach
the same height. In the case of the point( 0 , 2 )the function happened to be defined there. In the case of the point
( 1 , 1 )the function happened to be defined elsewhere, but that does not matter. You only need to consider what the
function does right around the point.
- Since you already know how to graph piecewise functions (graph each function in thexinterval indicated) you
can then observe graphically the limits at -2, 0 and 1.
xlim→− 2 f(x) =^2
limx→ 0 f(x) =DNE
limx→ 1 f(x) = 1
Practice
Use the graph off(x)below to evaluate the expressions in 1-6.
- limx→−∞f(x)
- limx→∞f(x)
- limx→ 2 f(x)
- limx→ 0 f(x)
5.f( 0 )
6.f( 2 )
Use the graph ofg(x)below to evaluate the expressions in 7-13.