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Solve the 5 question attached in the word doc ( please send answers in a word doc not PDF)

Attached PDF section 4.0 ( Solve problem 6)

Attached PDF section 4.7 ( Solve problem 7)

In problems 7 sketch the graph of each function and find the area between the graphs of f and g for x in the given interval. 7. f(x) = x 2 + 3 , g(x) = 1 and –1 ≤ x ≤ 2.

MATH 140 Quiz 5 NAME___________________________ INSTRUCTIONS • • • • • The quiz is worth 100 points. There are five problems (each worth 20 points). This quiz is open book and open notes. This means you may refer to your textbook, notes, and online classroom materials, but you may not consult anyone. You may take as much time as you wish, provided you turn in your quiz no later than the due date posted in our syllabus. You must show all work in order to receive full credit. If you do not show your work, you may earn only partial or no credit at the discretion of the professor. Please carefully review How to submit quizzes and exams in our Syllabus. If you have any questions, please feel free to send me a PAGER message in LEO. Emailed quizzes and exams will not be accepted (they crash my email system). Thank you for understanding. Best of luck! ☺ MULTIPLE CHOICE Select the best answer choice. Write your answer choices below: (1) _____ (2) _____ (3) _____ (4) _____ (5) _____ 1) Evaluate (1) _____ ∫ (𝐴) 1 1 cos ( ) 𝑑𝑥 𝑥2 𝑥 1 1 sin ( ) 𝑥 𝑥 1 1 (𝐵) − sin ( ) + 𝐶 𝑥 𝑥 1 (𝐶) sin ( ) + 𝐶 𝑥 1 (𝐷) −sin ( ) + 𝐶 𝑥 (𝐸) 𝑁𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑏𝑜𝑣𝑒 2) Solve the initial value problem (2) _____ 𝑑𝑦 1 = , 𝑑𝑥 √𝑥 + 2 (𝐴) 1 √𝑥 + 2 𝑦(2) = −1 +1 (𝐵) 2√𝑥 + 2 − 1 (𝐶) 2√𝑥 + 2 − 5 (𝐷) 1 2√ 𝑥 + 2 +2 (𝐸) 𝑁𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑏𝑜𝑣𝑒 3) Given 𝑓(𝑥) = 𝑥 2 + 3, find the exact area 𝐴 of the region under 𝑦 = 𝑓(𝑥) on the interval [1, 3] by first computing the sum 𝑛 ∑ 𝑓(𝑥𝑘 )∆𝑥 𝑘=1 and then taking the limit as 𝑛 → ∞. Hint: ∑𝑛𝑘=1 𝑘 2 = 𝑛(𝑛+1)(2𝑛+1) 6 (3) _____ (Note: If limits are not used correctly, the maximum number of points possible for this problem will be 5 points out of 20 points.) (𝐴) 14 (𝐵) 44 3 (𝐶) 13 (𝐷) 56 3 (𝐸) 𝑁𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑏𝑜𝑣𝑒 5 4) Evaluate ∫0 (2𝑥 3 − 4𝑥 2 + 1)𝑑𝑥 by computing the limit 𝑛 lim ∑ 𝑓(𝑥𝑘 )∆𝑥 𝑛→∞ 𝑘=1 (Note: If limits are not used correctly, the maximum number of points possible for this problem will be 5 points out of 20 points.) (4) _____ (𝐴) 905 6 (𝐵) 875 6 (𝐶) 145 3 (𝐷) 𝑥 4 4𝑥 3 − +𝑥+𝐶 2 3 (𝐸) 𝑁𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑏𝑜𝑣𝑒 5) Evaluate (5) _____ 4 ∫ 1 (𝐴) − (𝐵) 1 2 1 2 (𝐶) − 2 (𝐷) 2 (𝐸) 𝑁𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑏𝑜𝑣𝑒 1 √𝑥 𝑑𝑥

JesseCraig
School: Purdue University

Attached.

1

CALCULAS
Student name:
Course:
Institution affiliation:

CALCULAS

2
CALCULAS

Problem 6 (PDF section 4.0)
a) Area = area of trapezium + area of triangle
= ½ (a+b)h + ½ bh
= ½ (2+1)2 + ½ *1*1
= 3.5 in2
b) The area of the shaded region in Fig. 24b is greater than the area of the shaded region in
part a.

Problem 7 (PDF section 4.7)
f (x) = x2 + 3, g(x) = 1 and -1≤ x ≤ 2

f(x) ≥ g(x)
2
Thus,

2
∫−1[(𝑥 2

+ 3) − 1] = [(x /3 + 3x) – x]
3

-1
= [(2 /3 + 3*2) – 2] – [(-13/3 + 3*-1) - -1]
3

= 20/3 – (-7/3)
= 20/3 + 7/3
= 9 in2

Running head: MATH 140 Quiz 5

1

MATH 140 Quiz 5
Student name:
Course:
Institution affiliation:

MATH 140 Quiz 5
MATH 140 Quiz 5

2
NAME___________________________

INSTRUCTIONS

The quiz is worth 100 points. There are five problems (each worth 20 points).
This quiz is open book and open notes. This means you may refer to your textbook,
notes, and online classroom materials, but you may not consult anyone. You may take as
much time as you wish, provided you turn in your quiz no later than the due date posted
in our syllabus.
You must show all work in order to receive full credit. If you do not show your
work, ...

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Anonymous
Excellent job

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