Explanation Given information: Given function: f ( x ) = x Formula used: Slope of a secant line from ( 0 , 0 ) to ( x , f ( x ) ) is given by f ( x ) − f ( 0 ) x − 0 Calculations: Given function can be written as f ( x ) = ( x ) 1 2 . At x = 0 , 1 f ( 1 ) = ( 1 ) 1 2 = 1 f ( 0 ) = ( 0 ) 1 2 = 0 The slope of the secant line from ( 0 , 0 ) to ( 1 , f ( 1 ) ) is f ( 1 ) − f ( 0 ) 1 − 0 = 1 − 0 1 = 1 At x = 0.1 f ( 0.1 ) = ( 0.1 ) 1 2 = 0.316 The slope of the secant line from ( 0 , 0 ) to ( 0.1 , f ( 0.1 ) ) is f ( 0.1 ) − f ( 0 ) 0.1 − 0 = 0.316 − 0 0.1 = 3.16 At x = 0 To determine (b) The slope of tangent line at 0. To determine (c) To plot: The graph of f ( x ) = x near x = 0 and explain it.

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

4th Edition

ISBN: 9781319312886

Author: Rogawski, Jon, Adams, Colin, FRANZOSA, Robert

Publisher: W. H. Freeman

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 2.1, Problem 23E

To determine

(a)

To slope of secant line from (0,0) to (x,f(x)) for x=1,0.1,0.01,0.001,0.0001.

To determine

(b)

The slope of tangent line at 0.

To determine

(c)

To plot:

The graph of f(x)=x near x=0 and explain it.

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Chapter 2.1, Problem 22E

Chapter 2.1, Problem 24E

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Chapter 2 Solutions

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

Ch. 2.1 - Prob. 1PQ Ch. 2.1 - Prob. 2PQ Ch. 2.1 - Prob. 3PQ Ch. 2.1 - Prob. 4PQ Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E

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(a) To slope of secant line from ( 0 , 0 ) to ( x , f ( x ) ) for x = 1 , 0.1 , 0.01 , 0.001 , 0.0001.

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(a) To slope of secant line from (0,0) to (x,f(x)) for x=1,0.1,0.01,0.001,0.0001.

(b) The slope of tangent line at 0.

(c) To plot: The graph of f(x)=x near x=0 and explain it.

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Chapter 2 Solutions

(a)

To slope of secant line from (0,0) to (x,f(x)) for x=1,0.1,0.01,0.001,0.0001.

(b)

The slope of tangent line at 0.

(c)

To plot:

The graph of f(x)=x near x=0 and explain it.