(a) Explanation Let us define a function f : R → R f ( x ) = x Now, let us define an interval [ 0 , x ] .Since, f ( x ) = x is polynomial function and therefore, is continuous on ( 4 , x ) and differentiable on [ 4 , x ] . It is evident from the function, f ( x ) = x that f ( 4 ) = 2 From Mean Value Theorem f ' ( w (b) To determine The proof of x < 1 + x 4 provided that x > 4

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…

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Chapter 4.2, Problem 48PS

(a)

To determine

The proof that there is a number ‘w’ between 4 and ‘x’ for which x−2x−4=12w provided that x>4

(b)

To determine

The proof of x<1+x4 provided that x>4

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Chapter 4.2, Problem 47PS

Chapter 4.2, Problem 49PS

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Chapter 4 Solutions

Student's Solution and Survival Manual for Calculus

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The proof that there is a number ‘w’ between 4 and ‘x’ for which x − 2 x − 4 = 1 2 w provided that x > 4

Solution Summary: The author explains the proof that there is a number ‘w’ between 4 and ‘x’.

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The proof that there is a number ‘w’ between 4 and ‘x’ for which x−2x−4=12w provided that x>4

The proof of x<1+x4 provided that x>4

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Chapter 4 Solutions

The proof that there is a number ‘w’ between 4 and ‘x’ for which x − 2 x − 4 = 1 2 w provided that x &gt; 4

Solution Summary: The author explains the proof that there is a number ‘w’ between 4 and ‘x’.

Concept explainers

Videos

The proof that there is a number ‘w’ between 4 and ‘x’ for which x−2x−4=12w provided that x>4

The proof of x<1+x4 provided that x>4

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Chapter 4 Solutions

The proof that there is a number ‘w’ between 4 and ‘x’ for which x − 2 x − 4 = 1 2 w provided that x > 4