Limits of a Piecewise Function In Exercises 31 and 32, sketch the graph of f. Then identify the values of c for which lim x → l f ( x ) exists. f ( x ) = { x 2 , x ≤ 2 8 − 2 x , 2 < x < 4 4 , x ≥ 4
Limits of a Piecewise Function In Exercises 31 and 32, sketch the graph of f. Then identify the values of c for which lim x → l f ( x ) exists. f ( x ) = { x 2 , x ≤ 2 8 − 2 x , 2 < x < 4 4 , x ≥ 4
Solution Summary: The author explains that the given function splits into three polynomials, and the limit of the function exists for all values except c = 4. As x approaches 2 from left or right, f (x) approaches 0,
Limits of a Piecewise Function In Exercises 31 and 32, sketch the graph of f. Then identify the values of c for which
lim
x
→
l
f
(
x
)
exists.
f
(
x
)
=
{
x
2
,
x
≤
2
8
−
2
x
,
2
<
x
<
4
4
,
x
≥
4
Definition Definition Group of one or more functions defined at different and non-overlapping domains. The rule of a piecewise function is different for different pieces or portions of the domain.
Sketch the graph of an example of a function f that satisfies all of the given conditions.
lim x→−1− f(x) = 0, lim x→−1+ f(x) = 1, lim x→2 f(x) = 3, f(−1) = 4, f(2) = 0
Let f(x)=2x+1 and g(x)=x2-1. What is the composition (f of g)(x)?
Limits of Rational FunctionsIn Exercises 13–22, find the limit of each rational function (a) as
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