Mathematics Homework Help

I’m working on a calculus discussion question and need support to help me learn.

THIS IS A THREE IN ONE DISCUSSION ASSIGNMENT. IT CONTAINS MODULE 7, MODULE 8 AND MODULE 9 DISCUSSION. Please kindly solve differently or number them separately when solving.

1. For this discussion, you will work in groups to find the area and answer questions.

Find the approximate area under the curve by dividing the intervals into $$subintervals and then adding up the areas of the inscribed rectangles. The height of each rectangle may be found by evaluating the function for each value of x. Your instructor will assign you 1${}_{\mathrm{}}$and 2${}_{\mathrm{}}$.

• =2 2+1‾‾‾‾‾‾√$\mathrm{}\sqrt{{}^{\mathrm{}}\mathrm{}}$ between =0$\mathrm{}$ and =6$\mathrm{}$ for 1${}_{\mathrm{}}$and 2${}_{\mathrm{}}$
• Find the exact area under the curve using integration =2 2+1‾‾‾‾‾‾√$\mathrm{}\sqrt{{}^{\mathrm{}}\mathrm{}}$between =0$\mathrm{}$ and =6$\mathrm{}$

Explain the reason for the difference in your answers.

2.For this discussion, you will work in groups to visualize the area under a curve using the online graphing tool Desmos. You will use the Desmos applet for a definite integral. To get started:

• First, review the Learn Desmos: Integrals video (desmos 1:51) (Links to an external site.) for a few pointers on using Desmos.
• Then, access the Definite Integral tool (Links to an external site.) from the Desmos site as a guest. You don’t need to create an account or sign in to the site.

Use the Definite Integral tool to explore the area under a curve. Complete the following.

• Replace the default equation with ( )=3 5−2 3$\mathrm{}{}^{\mathrm{}}\mathrm{}{}^{\mathrm{}}$.
• First, set the limits as =1$\mathrm{}$ and =2$\mathrm{}$. You may need to zoom in or out to see the graph and the shaded region.
• Then, experiment with a and b both being negative.
• Then, let a be negative and b be positive. Try using the slider and have a and b as decimals.
• Take a screenshot of one of your cases (including the right column of input information and the graph with the shaded region) to post into the discussion.

Find & Post

Find ∫21(3 5−2 3) ${}_{\mathrm{}}^{\mathrm{}}\mathrm{}{}^{\mathrm{}}\mathrm{}{}^{\mathrm{}}$ and share the steps you used to get it.

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Post your step-by-step work and a screenshot of one of your cases.

Question 3.

Find an equation for the slant asymptote for the rational function below

$f\left(x\right)=\frac{-3x^2-5x^3+x+3}{x^2-x+3}$