Category: Calculus

Access the help on integrals (Desmos) Links to an external site. and review the first example in the section about indefinite integrals. This example demonstrates the method of graphing antiderivative of the sample function f(x) = x^2. The outcome is the graph of F(x) = x^3/3.
In Desmos, graph the first derivative function from your application problem in Discussion 6. Then using the integral notation as shown in the above example, graph its antiderivative so that the maximum value of the antiderivative function is twice as great as the maximum value of your function (c) from Discussion 1.
Using the graph of the antiderivative function, estimate the -intercept and the end value of the function (as x –> + infinity).
Interpret the y-intercept and the end behavior of the antiderivative function in the context of your application problem.

I have a total of 18 brief questions from my open-source math (subject Calculus). Sample of questions is attached.

In one to two sentences, formulate an application problem that could
be modeled mathematically through the graph of the function (c) from Discussion 1. Some examples are the cost functions (manufacturing, production, distribution, transportation, installation, setup, etc.),
economy charts, population functions, and modeling an epidemic. Be sure
to indicate what entities are represented by independent and dependent
variables.
Include the following:For
what values of the independent variable does the function have a
practical interpretation in the context of your application problem?
Explain.
In Desmos, draw the graph of the first derivative function 0 and interpret it in the context of your application problem.
Find all values for which the first derivative of the function 0 is and interpret them in the context of your application problem.

Given the following price-demand function, find the elasticity of demand, E(p), and determine whether demand is elastic, inelastic, or has unit elasticity for the following values of p. (Round your answers to two decimal places.)
x = 303,750 − 50p2
(a)p = 34
E(p) =
(b)p = 60
E(p) =
(c)p = 50
E(p) =
And say wether it is elastic, inelastic, or has unit elasticity for the following values of p

I had to copy and paste my questions; I hope they are clear for you to read. For some reason it was letting upload a file without giving me a 0 error code. Need full answers and how to. 1. Write the domain and range of the function using interval notation.
domain range
2. Use the graph of the function to estimate the intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.)
increasing decreasing
3. Consider the graph shown below.
Estimate the intervals where the function is increasing or decreasing. (Enter your answers using interval notation.)
increasing decreasing
4. Use the graph of the function to estimate the local maximum and local minimum of the function. (Round your answer to two decimal places. If an answer does not exist, enter DNE.)
maximum (x, y) = minimum(x, y) = 5. Consider the graph shown below.
If the complete graph of the function is shown, estimate the intervals where the function is increasing or decreasing. (Enter your answers using interval notation.)
increasing decreasing
6. Use the graph of the function to estimate the local maximum and local minimum of the function. (Round your answer to two decimal places. If an answer does not exist, enter DNE.)
maximum (x, y) =
minimum(x, y) = 7.The graphs of the functions f(x)
and g(x)
are shown below.
(a) Find (f · g)(1).
(f · g)(1) = (b) Find (f − g)(0).
(f − g)(0) = 8. Use the graph of f, shown below, to evaluate the expression.
f(f(5))

1. I invest $100,000 in a company for five years, with a guaranteed income of 8% per year, compounded semi-annually. How much will I have at the end of 5 years? If the interest were compounded continuously, how much would I have in 5 years?

1. A certain element decays at a rate of 000163/year. Of a piece of this element of 450 kg, how much will remain in ten years?
2. Two variables are related by the equation 2 inx+ Iny-y. What is the equation of the tangent line to the graph of this relation at the point (1.1)?3.i invest $100,000 in a company for five years, with a guaranteed income of 8% per year, compounded semi-annually. How much will I have at the end of 5 years? If the interest were compounded continuously, how much would I have in 5 years?

This discussion re-visits the concept of a function. You will explore the online graphing tool Desmos and graph algebraic functions.
Access the attached Desmos User Guide and review all sections except for Regressions.
Use Desmos (https://www.desmos.com/calculator) to graph three assigned functions, as follows: Start by graphing either y = 1/x or y = 1/x^2 and modify that function to create the graphs of three other algebraic functions with the following properties:
a. one vertical asymptote (no horizontal asymptote)
b. one horizontal and two vertical asymptotes
c. one horizontal asymptote (no vertical asymptote). Ensure that the entire function 2c is in the positive halfplane.
3. Using the graph of each function, state the domain and range, and write the equations of the horizontal and vertical asymptotes.
4. In five to ten sentences, explain your rationale for determining the domain, the range, and the asymptotes from the graph. What ideas have you studied previously that were useful in the analysis?

3 sperate math hw assignments about 8 questions each should not take very long, pretty straigt forward

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