A graphing calculator is recommended. Find the Gini index for the given Lorenz curve. (Round your answer to three decimal places.)   L(x)=(3x + x2 + x3)/5

Q: -(x) u'00-x n(x) = -2(x-3)(3x-2)°(r+4) Determine the end behavior of the graph of the function.

A: We will use limit to find the results

Q: 5. Give an example of a 4th-degree polynomial function, P(x), whose graph on a Cartesian coordinate…

A: Clearly it has been specified that the function should not have any X-axis intercept which is…

Q: Solve for x. log,(x² – 4) – log4(x+2) =2

A: Solve for x -> log4(x2-4)-log4(x+2)=2

Q: Evaluate the given function.   f(x)=log3x               ​a) ​ f(27​) b) ​ f(81​)

A:

Q: Choose the graph of y = log2() from the given choices below. -2 Cole

A:

Q: Let h(x) = x - 3 and g(x)= 8x. Find the following. |(x) |(x) =, x# (Simplify your answer.)

A: Given: h(x)=x-3 g(x)=8x

Q: a. f(z) = – log:(z) = - 3 b. f(z) = log3(x) c. f(x) = - log;() d. f(x) = log:() %3D 3

A: Given: a. f(x)=-log13x b. f(x)=log3x c. f(x)= -log5x d. f(x)=log13x

Q: Let f(1) = 2/L. If g(z) is the graph of f(r) shifted up 1 units and right 5 units, write a formula…

A: The vertical shift in the graph of y=f(x) is represented by the transformation function, y=f(x)±n…

Q: Suppose f(x) = log(Va- 5) and g(x domain of (f – g)(x). T-25 %3D State the x2-30x ||

A: In the given question, the concept of domain is applied. Domain The set of a function's available…

Q: y = f (x) = -3 – 3 * log 1 (-4x + 8) %3D 1. Sketch its graph 2. Specify its D and R 3. Find the…

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want…

Q: 1. Below shows the graph of y=2* ,sketch the graph of (a) y=(-2) (b) y= log₂ x (c) y= log₁x 2 -4 -3…

A: Solution:-

Q: Which of the graphs below could be the graph of a power function with an even power? (a) ☐ (b) ☐ (c)…

A: To identify which of the given graphs is a graph of a power function with an even power. Concepts…

Q: Consider the graph of the function y= 1 - 0.333333x  What is the x intercepct on this graph?

A:

Q: Suppose f(x)= log(x) and f(2)= 8. Determine the function value. 2. (1) a. (1)-0 b. f(16) (Simplify…

A: The given function is  and

Q: 4. Find all the values of z for which each equation holds. (a) Log(z - 1) = -i.

A:

Q: )at a: is. sin acos e The deriva tive of a functian: y=logg

A:

Q: 10

A:

Q: Compare the functions f(x) = x³ and g(x) = ex by graphing both functions in several viewing…

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.