Total Cost and Riemann Sums: MATH 154 Assignment Insights
School
University of Alberta**We aren't endorsed by this school
Course
MATH 154
Subject
Mathematics
Date
Dec 11, 2024
Pages
7
Uploaded by GeneralKookaburaPerson1257
MATH 154, Fall 2024, Written Assignment 8Please submit your full solutions before 4:00pm onSunday, December 1 through Assign2.Note:You must show all your workings to get full marks.1.[3+2=5 points]A division of Ditton Industries manufactures a deluxe toaster oven.Management has determined that the daily marginal cost function associated withproducing these toaster ovens is given byC0(x) = 0.000006x2-0.002x+ 6,whereC0(x) is measured in dollars per unit andxdenotes the number of units pro-duced.Management has also determined that the daily fixed cost incurred in theproduction is$4000.(a) Find the total cost incurred by Ditton in producing the first 1000 units of thesetoaster ovens per day.(b) What is the total cost incurred by Ditton in producing the 501st through 1000thunits/day?2.[1+2+2=5 points]Letf(x) =x2+x+ 1.(a) ExpressZ1-2(x2+x+ 1)dxas limits of Riemann sums. Do not evaluate the limit.(b) Sketch the regionRcompletely enclosed by the graph offand the vertical linesx=-2 andx= 1, and use a Riemann sum with six subintervals of equal length(n= 6) to approximate the integralZ1-2f(x)dx.(c) Evaluate the integral in part (a) using the Fundamental Theorem of Calculus.3.[5 points]EvaluateZ5-2(5-|x|)dxby interpreting in terms of areas.4.[3+2=5 points](a) Find the area of the region enclosed by:y= sinx,andy=-cosx,over the interval [0,⇡].(b) Evaluate the following integral:Zx3p1-x2dx1
