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.
After a great deal of experimentation, two college senior physics majors determined that when a bottle of French champagne is shaken several times, held upright, and uncorked,
its cork travels according to the function below, where s is its height (in feet) above the ground t seconds after being released.
s(t)=-16t² + 30t+3
a. How high will it go?
b. How long is it in the air?
+6x²+135x+1) (0≤x≤10). a) Find the number of units
The total profit P(x) (in thousands of dollars) from a sale of x thousand units of a new product is given by P(x) = In (-x²+6x² + 135x+
that should be sold in order to maximize the total profit. b) What is the maximum profit?
The fox population in a certain region has an annual growth rate of 8 percent per year. It is estimated that the
population in the year 2000 was 22600.
(a) Find a function that models the population t years after 2000 (t = 0 for 2000).
Your answer is P(t)
=
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer should be an integer)
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