Explanation Given information: The function y = tanh − 1 x at x = 0 Concept used: Linear approximation of function: A linear approximation f 1 of function f at x = a is, f 1 = f ( a ) + f ′ ( a ) . ( x − a ) d d x t a n h − 1 ( x ) = 1 1 − x 2 Einstein Law: By this law relative velocity is, tanh − 1 w c = tanh − 1 u c + tanh − 1 v c Here, c = 3 × 10 8 m/sec , is the velocity of light. Galileo Law: By this law relative velocity is, w = u + v w = Relative velocity, u = velocity of the object and v = velocity of the train

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 7.7, Problem 46E

To determine

To prove: That the linearization of the function y=tanh−1x at x=0 is tanh−1x≈x . With the help of tanh−1x≈x show that Einstein’s law of velocity addition reduces to Galileo’s law if the velocities are small relative to the speed of light.

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Chapter 7.7, Problem 45E

Chapter 7.7, Problem 47E

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Chapter 7 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

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To prove: That the linearization of the function y = tanh − 1 x at x = 0 is tanh − 1 x ≈ x . With the help of tanh − 1 x ≈ x show that Einstein’s law of velocity addition reduces to Galileo’s law if the velocities are small relative to the speed of light.

Solution Summary: The author proves that the linearization of the function y=mathrmtanh-1xapprox x is based on Einstein's law of velocity addition.

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To prove: That the linearization of the function y=tanh−1x at x=0 is tanh−1x≈x . With the help of tanh−1x≈x show that Einstein’s law of velocity addition reduces to Galileo’s law if the velocities are small relative to the speed of light.

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