Concept explainers
78.
(a) Determine whether G is even, odd, or neither.
(b) There is a
(c) Suppose the area under the graph of G between and that is bounded from below by the axis is 1612.8 square units. Using the result from part (a), determine the area under the graph of G between and that is bounded from below by the .
a. Check whether the function is even, odd or neither.
Answer to Problem 74AYU
a. The given function is an even function.
Explanation of Solution
Given:
The function .
Calculation:
It is asked to check the whether the function is even, odd or neither and find the second local maximum value based on the local maximum value of 25 at . Also find the area under the graph of between and that is bounded from below by the using the area under the graph of between and that is bounded from below by the is square units.
By the definition of odd and even function,
“A function is even if, for every number in its domain, the number is also in the domain and ” and
“A function is odd if, for every number in its domain, the number is also in the domain and ”.
“A function is even if and only if, whenever the point is on the graph of , the point is also on the graph.
a. Consider the function,
Replace by ,
From the statement, it can be concluded that the given function is an even function.
b. The second local maximum value based on a local maximum given.
Answer to Problem 74AYU
b. The second local maximum value based on the local maximum value of 400 at is .
Explanation of Solution
Given:
The function .
Calculation:
It is asked to check the whether the function is even, odd or neither and find the second local maximum value based on the local maximum value of 25 at . Also find the area under the graph of between and that is bounded from below by the using the area under the graph of between and that is bounded from below by the is square units.
By the definition of odd and even function,
“A function is even if, for every number in its domain, the number is also in the domain and ” and
“A function is odd if, for every number in its domain, the number is also in the domain and ”.
“A function is even if and only if, whenever the point is on the graph of , the point is also on the graph.
b.There is a local maximum value of 400 at . Therefore, the local maximum point is .
The definition of even function says that whenever the point is on the graph of , the point also on the graph.
From this, the second local maximum point must be .
c. The area under the graph of between and that is bounded from below by the using the area under the graph of between and that is bounded from below by the is square units.
Answer to Problem 74AYU
c. The area under the graph of between and that is bounded from below by the is .
Explanation of Solution
Given:
The function .
Calculation:
It is asked to check the whether the function is even, odd or neither and find the second local maximum value based on the local maximum value of 25 at . Also find the area under the graph of between and that is bounded from below by the using the area under the graph of between and that is bounded from below by the is square units.
By the definition of odd and even function,
“A function is even if, for every number in its domain, the number is also in the domain and ” and
“A function is odd if, for every number in its domain, the number is also in the domain and ”.
“A function is even if and only if, whenever the point is on the graph of , the point is also on the graph.
c. The area under the graph of between and that is bounded from below by the is square units.
As the function is even from result (a), there must be another same area under the same graph between and that is also bounded from below by the .
Therefore the area under the graph of between and that is bounded from below by the square units.
Chapter 2 Solutions
Precalculus Enhanced with Graphing Utilities
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