# Asymptotic behavior

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Question description

Please provide complete steps for solutions including graph when neccessary.

ASYMPTOTIC BEHAVIOR OF FUNCTIONS

7x143 + 734x – 2 x150 – 99x83 + 25

MATH 140 Quiz 4 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. 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. 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) I. _____ II. _____ III. _____ (2) _____ (3) _____ (4) _____ (5) _____ 1) Match each of the following graphs to the appropriate conditions for 𝑓′ and 𝑓′′. Explain. I. 𝑦 = 𝑓(𝑥) 0 1 2 II. 𝑦 = 𝑓(𝑥) 0 1 2 III. 𝑦 = 𝑓(𝑥) 0 1 2 A. 𝑓 ′ (𝑥) > 0 𝑜𝑛 (0, 2), 𝑓 ′′ (𝑥) < 0 𝑜𝑛 (0, 1), 𝑓 ′′ (𝑥) > 0 𝑜𝑛 (1, 2) B. 𝑓 ′ (𝑥) > 0 𝑜𝑛 (0, 1), 𝑓 ′ (𝑥) < 0 𝑜𝑛 (1, 2), 𝑓 ′′ (𝑥) > 0 𝑜𝑛 (1, 2), 𝑓 ′′ (𝑥) < 0 𝑜𝑛 (1, 2) C. 𝑓 ′ (𝑥) > 0 𝑜𝑛 (0, 1), 𝑓 ′ (𝑥) < 0 𝑜𝑛 (1, 2), 𝑓 ′′ (𝑥) > 0 𝑜𝑛 (0, 2) D. 𝑓 ′ (𝑥) > 0 𝑜𝑛 (0, 1), 𝑓 ′ (𝑥) < 0 𝑜𝑛 (1, 2), 𝑓 ′′ (𝑥) < 0 𝑜𝑛 (0, 2) E. 𝑓 ′ (𝑥) < 0 𝑜𝑛 (0, 1), 𝑓 ′ (𝑥) > 0 𝑜𝑛 (1, 2), 𝑓 ′′ (𝑥) < 0 𝑜𝑛 (0, 1), 𝑓 ′′ (𝑥) > 0 𝑜𝑛 (1, 2) Write the letter that corresponds to the correct graph: (I) __________ (II) __________ 2) Find the critical numbers for the function (III) __________ 𝑓(𝑥) = 2𝑥 √𝑥 − 1 (A) 𝑥 = 0, (B) 𝑥 = 0, 𝑥 = 1 (C) 𝑥 = 2 (D) 𝑥 = 1, 𝑥 = 2 (E) None of the above 2) _____________ 3) Find the intervals on the 𝑥-axis on which the function 𝑓(𝑥) is increasing and those on which it is decreasing, where 𝑓(𝑥) = 𝑥2 − 1 𝑥2 + 1 3) ______________ (A) Decreasing on (−∞, 0); Increasing on (0, ∞). (B) Increasing on (−∞, 0); Decreasing on (0, ∞). (C) Increasing on (−∞, −1); Increasing on (1, ∞); Decreasing on (−1, 1). (D) Decreasing on (−∞, −1); Increasing on (−1, 1); Decreasing on (1, ∞). (E) None of the above 4) Find the maximum value of the function 𝑓(𝑥) = 𝑥 2 + 9𝑥 − 3 𝑥2 4) (A) 2/3 (B) 1 (C) 7.75 (D) 16 (E) None of the above _____________ 5) Engineers want to design an auxiliary pipeline from a new natural gas source; 3 km from the main pipeline, to a power plant located 10 km down the main pipeline, in the least amount of time (see Figure 1). If the oil can flow 10 km/hr along the auxiliary pipeline (OB) and 15 km/hr along the main pipeline (AP), where should the engineers join the auxiliary pipeline to the main pipeline to get the gas to P as soon as possible? Figure 1 Natural Gas Source O 3 A B P x Power Plant 10 – x 10 5) (A) 0 (B) 0.89 (C) 0.97 (D) 6/√5 (E) None of the above _____________

School: Cornell University

Attached.

MATH 140 Quiz 4

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. 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.
If you have any questions, please feel free to send me a PAGER message in LEO.
Emailed qui...

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Anonymous
Thanks, good work

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