Explanation Given information: A limit function is given as, lim x → 0 + 1 − cos 2 x sin 3 x . Concept used: L'Hospital's Rule: If f and g are differentiable in an open interval containing a and f ( a ) = g ( a ) = 0 . Also, g ' ( x ) ≠ 0 (except possibly at a ). Then- lim x → a f ( x ) g ( x ) = lim x → a f ' ( x ) g ' ( x ) This rule is also applicable when f ( a ) = ± ∞ and g ( a ) = ± ∞

6th Edition

ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 4.5, Problem 7PS

To determine

To calculate: The value of given limit.

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Chapter 4.5, Problem 6PS

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f'(x)

A body of mass m at the top of a 100 m high tower is thrown vertically upward with an initial velocity of 10 m/s. Assume that the air resistance FD acting on the body is proportional to the velocity V, so that FD=kV. Taking g = 9.75 m/s2 and k/m = 5 s, determine: a) what height the body will reach at the top of the tower, b) how long it will take the body to touch the ground, and c) the velocity of the body when it touches the ground.

Chapter 4 Solutions

Calculus

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The value of given limit.

Solution Summary: The author explains the L'Hospital's Rule for calculating the value of a given limit.

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Chapter 4 Solutions