Quiz 4 Instructions: Sections 31, 41, 42, 08

Quiz 4instructions This Quiz Covers Sections 31 41 42 08 And 4

This quiz covers Sections 3.1, 4.1, 4.2, 0.8, and 4.3. Please only use the Answer Sheet either to type your work or if you prefer to write your work and scan it. Be sure to include your name in the document. Consult the Additional Information portion of the online Syllabus for options regarding the submission of your quiz. If you have any questions, please contact me by e-mail ( [email protected] ) with MATH 107 in the subject heading. UMUC © Math – Fall 2019 OL1 Jules Kouatchou.

Paper For Above instruction

This assignment involves a series of mathematical problems designed to test your understanding of various calculus concepts, including the Intermediate Value Theorem, domain analysis, asymptotic behavior, and basic algebraic problem-solving. You are instructed to utilize the Answer Sheet to either type your solutions or write and scan your handwritten work. It is imperative to include your name on the document to ensure proper identification for grading purposes.

First, you will employ the Intermediate Value Theorem to determine whether a specified function has a zero within a given interval. This requires analyzing the function values at the endpoints of the interval and checking for a change in sign, which indicates the existence of at least one zero in that interval. Understanding this theorem is fundamental for analyzing continuous functions and their zeros, a core concept in calculus.

Next, you will analyze a different function by finding its domain, identifying its vertical asymptote(s), and horizontal asymptote(s). Domain determination involves identifying all input values for which the function is defined, excluding any that cause division by zero or other undefined operations. Vertical asymptotes correspond to vertical lines where the function tends to infinity, often due to division by zero, while horizontal asymptotes describe the end behavior of the function as x approaches infinity or negative infinity. These analyses are crucial for understanding the behavior and limitations of functions in calculus.

Subsequently, you will find the real zeros of a given function, which are inputs where the function evaluates to zero. This often involves solving algebraic equations or applying factoring techniques. Then, you will work through solving specific algebraic problems, possibly involving quadratic equations or other polynomial functions, reinforcing skills in solving for unknowns.

Additional word problems include determining two numbers where one is six less than the other, and their product equals 72. This requires translating word statements into equations and solving for the variables involved. Another problem involves performing and simplifying an algebraic operation, likely to review skills in manipulating expressions.

Furthermore, you are asked to solve a work-rate problem: Jules and his son roofing a house simultaneously, with Jules taking 24 hours and his son 40 hours individually. Calculating their combined work rate involves summing their individual rates and determining the total time required for both working together. This problem showcases applications of rates and proportions in a real-world context.

Throughout this quiz, you are expected to show your work for all problems, as partial credit relies on your demonstrated understanding and process. This combination of theoretical and applied problems aims to strengthen your calculus and algebra skills essential for success in the course.

References

• Anton, H., Bivens, I., & Davis, S. (2013). Calculus: Early Transcendentals (10th ed.). John Wiley & Sons.
• Setzer, S. (2018). Algebra and Trigonometry. OpenStax. https://openstax.org/details/books/algebra-and-trigonometry
• Lang, S. (2002). Undergraduate Analysis. Springer-Verlag.
• Thomas, G. B., & Finney, R. L. (2002). Calculus and Analytic Geometry. Addison Wesley.
• Strang, G. (2016). Introduction to Linear Algebra (5th ed.). Wellesley-Cambridge Press.
• Marino, A. A. (2014). Applied Calculus for Business, Economics, and the Social and Life Sciences. Pearson.
• Rudin, W. (1976). Principles of Mathematical Analysis. McGraw-Hill.
• Fletcher, C. A. (2020). Differential Calculus. Springer.
• Sullivan, M. (2016). Calculus: Early Transcendentals. Pearson.
• Lay, D. C. (2012). Linear Algebra and Its Applications. Pearson.