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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)——————————————-

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