# Monmouth University Calculus Problems

Description

I have a 9 question quiz that needs to be done. It is MA118 and is only 9 questions, one or two of those questions might have 2 parts. One question asks for a graph, if the graph can be created on the computer then great if not a graph hand written will be accepted as well. Just send the graph as a picture or PDF to me. Besides that it should be fairly basic Calculus, just please show all work, be neat, and obviously the correwct answers as well. Thank you 🙂

MA-118
1)
2)
Find the anti-derivative for each of the following.
a)

∫(5𝑥 4 − 4𝑥 + 1) 𝑑𝑥
b)
∫ (𝑥 4 − √𝑥 + 4) 𝑑𝑥
5
a)————————————(4pts)
5
b)————————————–(4pts)
The marginal revenue function for a product is given by: 𝑀𝑅(𝑥) = 6𝑥 2 + 2𝑥 + 2
If the revenue from the sale of 6 items is \$100, find the revenue from the sale of 10 items.
Show all work or NO CREDIT!! (10pts)
2)————————————3) Find the anti-derivative of :
∫(3𝑥 4 − 6𝑥)9 (2𝑥 3 − 1)𝑑𝑥
Show all work or NO CREDIT!!! (8pts)
3)————————————————-
4) The production rate of an assembly line is given by:
Where t is the time in hours and
𝑑𝑅
𝑑𝑡
𝑑𝑅
𝑑𝑡
= 3𝑡 2 − 24𝑡 + 50
is the production rate per hour.
a) Use demos.com to draw the graph. Then copy the graph below. Approximate the
number of items produced during the first 8 hours by using LRAM with n=4. Show
all work including graph with rectangles or NO CREDIT!! (10pts)
a)———————————-b) Find the exact number of items produced during the first 8 hours by
Using the Fundamental theorem of Calculus. Show all work or NO CREDIT!!
(10pts)
b)————————————-
5) Find the cost of purchasing an annuity that pays \$35,000 per year for 30 years.
The interest rate is 2% and payments start in 5 years. SHOW ALL WORK OR NO
CREDIT!!! (16pts)
5)—————————————
6) Evaluate each definite integral. SHOW ALL WORK OR NO CREDIT!!!
3
a) ∫2 8𝑥 3 𝑑𝑥
5
b) ∫1 √4𝑥 + 5 4𝑑𝑥
c)
2
∫1 (3𝑥 2 − 6𝑥)2 (𝑥 − 1)𝑑𝑥
a)———————-(4pts)
b)———————-( 4pts)
c)————————(4pts)
7) The marginal revenue function for a product is given by: 𝑀𝐶(𝑥) = 90𝑒 0.04𝑥
Where x is the number of items produced and sold. Find the revenue function
and find the revenue from the sale of 10 items. Assume that 0 items produce
0 revenue. SHOW ALL WORK OR NO CREDIT!!! (10PTS)
Revenue function————————————-revenue from sale of 10 ———————-
8) Solve the differential equation:
𝑑𝑦
𝑑𝑥
=
12
𝑥2
− 6𝑥 2 + 2
with initial conditions (1, 10 ).
SHOW ALL WORK OR NO CREDIT!!! ( 8 pts)
8)————————————————9) The rate of depreciation for a piece of machinery is given by:
𝐷′ (𝑡) = 300,000𝑒 −0.01𝑡
Where t is the number of years after the purchase. Find the exact total depreciation for the
first three years by evaluating a definite integral. ( 8 pts )
9)——————————————-