MA 16100 Exam Instructions

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Questions and Answers

At what point(s) (x, y) on the graph of f(x) = x/(x + 5) does the tangent line to f(x) have a slope of 1/5?

There are no such points (correct)

(0, 0) and (-10, 2)

(0, 0) and (5, 1)

(10, 1/3) only

(0, 0) only

Find ∫ sin x cos x / (1 + sin² x) dx

*ln*(√(1 + *sin*² *x*)) + *C*

*tan*⁻¹(*sin* *x*) / 2 + *C* (correct)

*ln*|(1 + *sin* *x*)| + *C*

*ln*(1 + *sin*² *x*) + *C*

*tan*⁻¹(*sin* *x*) + *C*

If g(x) = ∫₀ˣ sin(2t) dt, then g'(x) =

6*x*² *sin*(2*x*³)

3*x*² *sin*(2*x*³) (correct)

*sin*(2*x*)

2*x*³ *sin*(2*x*³)

*sin*(2*x*³)

Which of the following statements are true about the function f(x) = x³ + x² - (1/12)x⁴ - 2x?

(I), (II), and (III) (B) Signup and view all the answers

A 5 foot ladder standing on level ground leans against a vertical wall. The bottom of the ladder is pulled away from the wall at 2 ft/sec. How fast is the AREA under the ladder changing when the top of the ladder is 4 feet above the ground?

-25/4 ft²/sec (A) Signup and view all the answers

Find the equation of the tangent line to the curve 2y⁴ - x²y = x³ at the point (1, 1).

y = x + 2/3 (A) Signup and view all the answers

Let f(x) = 5x² - 7x. Use the definition of the derivative to find f'(1). When you simplify the terms inside the limit, you get:

f'(1) = lim(3 + 3h) (A) Signup and view all the answers

Compute the limit: lim(x→0) (3eˣ - 1)/ sin x

3 (B) Signup and view all the answers

Consider a function f(x) defined such that ∫₃⁷ f(x) dx = 15, and ∫₇¹¹ f(x) dx = 11. What is ∫₃¹¹ 3f(x) dx?

-12 (C) Signup and view all the answers

Which of the following functions has lim(x→∞) f(x) = 2?

f(x) = (2x - 1)/(1 + 2x) (D) Signup and view all the answers

Suppose that lim(x→0) f(x) = ∞ and lim(x→0) g(x) = 0. What can be said about lim(x→0) f(x)g(x)?

The limit may or may not exist. If it exists, it can be any number (E) Signup and view all the answers

A rectangle with sides parallel to the axes is inscribed in the region above the x-axis and below the parabola y = 12 - x². The maximum area of such a rectangle is

24 (D) Signup and view all the answers

Find the limit. lim(x→2⁺) (ln x²)(tan(πx/4))

-∞ (B) Signup and view all the answers

Find the integral ∫ₑ⁴⁹ 1/(x ln(x)) dx

2 (A) Signup and view all the answers

Suppose f(x) = (x + 3)/(9 - x²). Then

lim(x→3⁻) f(x) = ∞ ; lim(x→3⁻) f(x) = 1/6 (B) Signup and view all the answers

Express the given quantity as a single logarithm: (3/2)ln(x + 4) + ln√(x) - (1/2)ln(x² + 10)

ln((x(x + 4)³) / (( x³ + 10) ^ (1/2)))* (C) Signup and view all the answers

A certain population of bacteria is growing exponentially. At time t = 0, there are 100 bacteria and at time t = 1 the population doubles to 200 bacteria. At what time will there be 300 bacteria present?

ln(3)/ ln2 (E) Signup and view all the answers

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Study Notes

Exam Instructions

The exam is for MA 16100
The exam is on 12/11/2023
Use the GREEN booklet
Write your name and student ID on the scantron
Use a #2 pencil for the scantron and fill in the correct information
Fill in your section number if known
Write the test/quiz number (11) on the scantron
Write your Purdue ID number with two leading zeros
There are 25 multiple choice questions worth 4 points each
Use the back of the test pages for scrap paper
Submit both the scantron and the exam booklet
If you finish early, you can leave after 9:50 AM
You must remain seated until your TA collects materials if you don't finish by 9:50 AM
No books, notes, calculators, or other electronics are permitted during the exam
You may not leave within the first 20 minutes or the last 10 minutes of the exam
Do not communicate with other students except with your TA
Put down all writing instruments after time is called

Exam Policies

Students may not open the exam booklet until instructed
Obey all proctors, TAs, and lecturers' orders and requests
No outside materials are allowed
Do not communicate with other students
Violations include severe penalties and reporting to the Office of the Dean of Students

Calculus Problems (Questions 1-8)

Question 1: Find points on the graph of f(x) = (x³ + 5) / (x + 5) where the tangent line has a slope of 2
Question 2: Evaluate the integral ∫ sin x cos x / (1 + sin² x) dx
Question 3: Given g(x) = ∫₀ˣ sin(2t) dt, find g'(x)
Question 4: Analyze the function f(x) = x³ + x² / (12 – 2x²)
Question 7: Use the definition of derivative to find f'(1) for f(x) = 5x² – 7x
Question 8: Compute the limit lim (3eˣ⁻¹ / sin x) as x approaches 0

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Description

Prepare for the MA 16100 exam on 12/11/2023 with these essential instructions. Ensure you have the correct materials and understand the policies for a smooth testing experience. Follow all guidelines regarding the use of personal items and communication during the exam.