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Calculus Examples
Popular Problems Calculus Find the Domain and Range f(x)=5x-3
f
(
x
)
=
5
x
−
3
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
(
−
∞
,
∞
)
Set-Builder Notation:
{
x
|
x
∈
R
}
The range is the set of all valid
y
values. Use the graph to find the range.
Interval Notation:
(
−
∞
,
∞
)
Set-Builder Notation:
{
y
|
y
∈
R
}
Determine the domain and range.
Domain:
(
−
∞
,
∞
)
,
{
x
|
x
∈
R
}
Range:
(
−
∞
,
∞
)
,
{
y
|
y
∈
R
}
is strictly increasing on [0, 5], so
and
so the integral is bounded between
Answer: total books = 180
Step-by-step explanation:
Given: Poetry section of the library has 6 bookcases.
Number of shelves in each bookcase = 3
Total shelves = (Number of shelves in each bookcase) x (Number of bookcases in each poetry section)
= 3 x 6
= 18
Number of books in each shelf = 10
Total books = (number of shelves) x 10
= 18 x 10
= 180
hence, total books in the poetry section= 180
