(a) Express the following limit of the Riemann 's sum as a definite integral and then evaluate the integral lim n-0 n

solve both algebraically and graphically x+y=4 y=3x

I attached a picture. I was able to do the simpler problems where you plug in a number for x (#1-4), but I do not remember how to set up the problem/equation once I have to use just x (#5-8). Once I learn that I think I will be able to do the problems in the second picture (a,b,c). Thank you!

solve problem number 26 on the photo attached below

Solve the problem below. For your initial post in Brightspace, copy the description of your company given in the box below and then enter your solution to all three parts (parts a, b, and c) of the problem. To copy the description of your company, highlighting and using "copy" from here in Mobius and then using "paste" into Brightspace should work. However, if when you copy and paste x you get a 2 instead, then change your x2 to x^2. Hint: We covered this topic in "2-1 Reading and Participation Activities: Quadratic Equations" in Module Two. You can check your answer to part b to make sure that you are on the right track. For a certain company, the cost for producing x items is 40x +300 and the revenue for selling a items is 80r - 0.5x2. The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit! Part a: Set up an expression…

I need to solve for #2