14.6. One Sided Limits and Continuity http://www.ck12.org
Example A
What are the one sided limits at -5, -1, 3 and 5?
Solution:
x→−lim 5 −f(x) =^1
x→−lim 5 +f(x) =^2
x→−lim 1 −f(x) =^2
x→−lim 1 +f(x) =^3
xlim→ 3 −f(x) =^3
xlim→ 3 +f(x) =−^2
xlim→ 5 −f(x) =−^2
x→−lim 5 +f(x) =DNE
Example B
Evaluate the one sided limit at 4 from the negative direction numerically.
f(x) =x^2 −x^7 −x 4 +^12
Solution:When creating the table, only use values that are smaller than 4.
TABLE14.11:
x 3.9 3.99 3.999
f(x) 0.9 0.99 0.999xlim→ 4 −
(x (^2) − 7 x+ 12
x− 4
)
= 1
Example C
Evaluate the following limits.
a. limx→ 3 −( 4 x− 3 )