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Problem

(a) Find the slope of the tangent to the curve $ …

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Problem 8 Easy Difficulty

Find an equation of the tangent line to the curve at the given point.

$ y = \dfrac{2x + 1}{x + 2} $, $ (1, 1) $


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03:39

Daniel Jaimes

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 7

Derivatives and Rates of Change

Related Topics

Limits

Derivatives

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TM

Tomas M.

October 4, 2020

Top Calculus 1 / AB Educators
Kayleah Tsai

Harvey Mudd College

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Lectures

Video Thumbnail

04:40

Limits - Intro

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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Watch More Solved Questions in Chapter 2

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61

Video Transcript

suppose you want to find an equation of the tangent line to the curve. Why? Which is equal to two? X plus one over X plus two. At the .1, 1 to do this, we first find the slope of the tangent line. That is the derivative of the function Evaluated at the given .1, 1. Now by quotient rule we have white prime, that's equal to X plus two times the derivative of the numerator two, x plus one-. We have to express one times the derivative of the denominator which is expressed to this all over the square of the denominator. And then from here we have X plus two Times derivative of to Express one. That's just too minus two, X plus one times the derivative of X plus two which is one. And then this all over the square of X plus two. And simplifying this, we have two, X plus four minus two, X -1. This all over X plus two squared or this is just three over the square of experts to And so the slope of the tangent line at the .11 is given by that's dy over dx evaluated at 1 1. This is just three over one plus two squared. That's just 3/9 or 1/3. So this is the slope of the tangent line at 11. And then the next step would be to use the point slope formula of a line to find the equation of the tangent line. Now the point slope formula of a line states that the the equation of the line is just why minus? Why is that one? This is equal to the slope mm Of that line times X -X. Sub one. Since you already have our point Except one White 1 Which is just 11. And we have our slope, we found out To be won over three. Then the equation of the tangent line is just Why -1 That's equal to 1/3 times x -1. And simplifying this, we have why that's equal to 1/3, X minus 1/3 Plus one. Or that why is equal to 1/3 Plus 2/3. And so this is the equation of the tangent line at the point 11

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Related Topics

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Kayleah Tsai

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Kristen Karbon

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Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Limits - Intro

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Join Course
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