learning-guide-unit-7-math-1211

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University of the People *

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1211

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Mathematics

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Jan 9, 2024

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Studocu is not sponsored or endorsed by any college or university Learning Guide Unit 7 -MATH 1211 Calculus (University of the People) Studocu is not sponsored or endorsed by any college or university Learning Guide Unit 7 -MATH 1211 Calculus (University of the People) Downloaded by Whitney turner (ct8682126@gmail.com) lOMoARcPSD|24613649

MATH 1211-01 Calculus - AY2023-T3  Dashboard  My courses  MATH 1211-01 - AY2023-T3  9 March - 15 March  Learning Guide Unit 7 Learning Guide Unit 7 Learning Guide Unit 7 Overview Unit 7: Newton’s Method, Antiderivative and L’Hopital’s Rule Topics:  L'Hopital's Rule  Newton’s Method  The Integral Downloaded by Whitney turner (ct8682126@gmail.com) lOMoARcPSD|24613649

Learning Objectives: By the end of this Unit, you will be able to: 1. Identify indeterminate forms with various operations and apply L’Hopital’s Rule 2. Apply Newton’s Method to find the roots of a polynomial. 3. Calculate the general antiderivative of a function. 4. Identify the iterative process and when Newton’s method does and does not work. Tasks:  Peer assess Unit 6 Written Assignment  Read the Learning Guide and Reading Assignments  Participate in the Discussion Assignment (post, comment, and rate in the Discussion Forum)  Complete and submit the Written Assignment  Make entries to the Learning Journal  Take the Self-Quiz Introduction Downloaded by Whitney turner (ct8682126@gmail.com) lOMoARcPSD|24613649

Image acquired from Calculus Volume 1, https://openstax.org/books/calculus-volume- 1@14.1/pages/4-9-newtons-method L’Hopital’s rule is powerful for evaluating limit problems that show indeterminate forms like or . Using this rule, we can find the limits of many functions that we couldn’t do before. You will see how the derivative makes it work. Newton’s method is also an application of the derivative. It allows us to approximate the roots of functions to a desired accuracy. Newton’s method is an iterative process, and by every step, we get closer to the actual root. This method uses the x-intercepts of the tangents. Although calculus's key concept is the derivative, which we learned so far in detail, now it’s time to learn about the antiderivative. The antiderivative is the reverse of the derivative (like “subtraction” is the reverse of “addition”). Like the derivative, the antiderivative also has many Downloaded by Whitney turner (ct8682126@gmail.com) lOMoARcPSD|24613649

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