Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 3.6, Problem 13PS
a.
To determine
To find the derivative of the given equation by implicit
b.
To determine
To find the derivative of the given equation by finding the explicit formula for y.
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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.
A chemical reaction involving the interaction of two substances A and B to form a new compound X is called a second order reaction. In such cases it is observed that the rate of reaction (or the rate at which the new compound is formed) is proportional to the product of the remaining amounts of the two original substances. If a molecule of A and a molecule of B combine to form a molecule of X (i.e., the reaction equation is A + B ⮕ X), then the differential equation describing this specific reaction can be expressed as:
dx/dt = k(a-x)(b-x)
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Chapter 3 Solutions
Calculus
Ch. 3.1 - Prob. 1PSCh. 3.1 - Prob. 2PSCh. 3.1 - Prob. 3PSCh. 3.1 - Prob. 4PSCh. 3.1 - Prob. 5PSCh. 3.1 - Prob. 6PSCh. 3.1 - Prob. 7PSCh. 3.1 - Prob. 8PSCh. 3.1 - Prob. 9PSCh. 3.1 - Prob. 10PS
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Prob. 1PSCh. 3.2 - Prob. 2PSCh. 3.2 - Prob. 3PSCh. 3.2 - Prob. 4PSCh. 3.2 - Prob. 5PSCh. 3.2 - Prob. 6PSCh. 3.2 - Prob. 7PSCh. 3.2 - Prob. 8PSCh. 3.2 - Prob. 9PSCh. 3.2 - Prob. 10PSCh. 3.2 - Prob. 11PSCh. 3.2 - Prob. 12PSCh. 3.2 - Prob. 13PSCh. 3.2 - Prob. 14PSCh. 3.2 - Prob. 15PSCh. 3.2 - Prob. 16PSCh. 3.2 - Prob. 17PSCh. 3.2 - Prob. 18PSCh. 3.2 - Prob. 19PSCh. 3.2 - Prob. 20PSCh. 3.2 - Prob. 21PSCh. 3.2 - Prob. 22PSCh. 3.2 - Prob. 23PSCh. 3.2 - Prob. 24PSCh. 3.2 - Prob. 25PSCh. 3.2 - Prob. 26PSCh. 3.2 - Prob. 27PSCh. 3.2 - Prob. 28PSCh. 3.2 - Prob. 29PSCh. 3.2 - Prob. 30PSCh. 3.2 - Prob. 31PSCh. 3.2 - Prob. 32PSCh. 3.2 - Prob. 33PSCh. 3.2 - Prob. 34PSCh. 3.2 - Prob. 35PSCh. 3.2 - Prob. 36PSCh. 3.2 - Prob. 37PSCh. 3.2 - Prob. 38PSCh. 3.2 - Prob. 39PSCh. 3.2 - Prob. 40PSCh. 3.2 - Prob. 41PSCh. 3.2 - Prob. 42PSCh. 3.2 - Prob. 43PSCh. 3.2 - Prob. 44PSCh. 3.2 - Prob. 45PSCh. 3.2 - Prob. 46PSCh. 3.2 - Prob. 47PSCh. 3.2 - Prob. 48PSCh. 3.2 - Prob. 49PSCh. 3.2 - Prob. 50PSCh. 3.2 - Prob. 51PSCh. 3.2 - Prob. 52PSCh. 3.2 - Prob. 53PSCh. 3.2 - Prob. 54PSCh. 3.2 - Prob. 55PSCh. 3.2 - Prob. 56PSCh. 3.2 - Prob. 57PSCh. 3.2 - Prob. 58PSCh. 3.2 - Prob. 59PSCh. 3.2 - Prob. 60PSCh. 3.3 - Prob. 1PSCh. 3.3 - Prob. 2PSCh. 3.3 - Prob. 3PSCh. 3.3 - Prob. 4PSCh. 3.3 - Prob. 5PSCh. 3.3 - Prob. 6PSCh. 3.3 - Prob. 7PSCh. 3.3 - Prob. 8PSCh. 3.3 - Prob. 9PSCh. 3.3 - Prob. 10PSCh. 3.3 - Prob. 11PSCh. 3.3 - Prob. 12PSCh. 3.3 - Prob. 13PSCh. 3.3 - Prob. 14PSCh. 3.3 - Prob. 15PSCh. 3.3 - Prob. 16PSCh. 3.3 - Prob. 17PSCh. 3.3 - Prob. 18PSCh. 3.3 - Prob. 19PSCh. 3.3 - Prob. 20PSCh. 3.3 - Prob. 21PSCh. 3.3 - Prob. 22PSCh. 3.3 - Prob. 23PSCh. 3.3 - Prob. 24PSCh. 3.3 - Prob. 25PSCh. 3.3 - Prob. 26PSCh. 3.3 - Prob. 27PSCh. 3.3 - Prob. 28PSCh. 3.3 - Prob. 29PSCh. 3.3 - Prob. 30PSCh. 3.3 - Prob. 31PSCh. 3.3 - Prob. 32PSCh. 3.3 - Prob. 33PSCh. 3.3 - Prob. 34PSCh. 3.3 - Prob. 35PSCh. 3.3 - Prob. 36PSCh. 3.3 - Prob. 37PSCh. 3.3 - Prob. 38PSCh. 3.3 - Prob. 39PSCh. 3.3 - Prob. 40PSCh. 3.3 - Prob. 41PSCh. 3.3 - Prob. 42PSCh. 3.3 - 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Prob. 16PSCh. 3.6 - Prob. 17PSCh. 3.6 - Prob. 18PSCh. 3.6 - Prob. 19PSCh. 3.6 - Prob. 20PSCh. 3.6 - Prob. 21PSCh. 3.6 - Prob. 22PSCh. 3.6 - Prob. 23PSCh. 3.6 - Prob. 24PSCh. 3.6 - Prob. 25PSCh. 3.6 - Prob. 26PSCh. 3.6 - Prob. 27PSCh. 3.6 - Prob. 28PSCh. 3.6 - Prob. 29PSCh. 3.6 - Prob. 30PSCh. 3.6 - Prob. 31PSCh. 3.6 - Prob. 32PSCh. 3.6 - Prob. 33PSCh. 3.6 - Prob. 34PSCh. 3.6 - Prob. 35PSCh. 3.6 - Prob. 36PSCh. 3.6 - Prob. 37PSCh. 3.6 - Prob. 38PSCh. 3.6 - Prob. 39PSCh. 3.6 - Prob. 40PSCh. 3.6 - Prob. 41PSCh. 3.6 - Prob. 42PSCh. 3.6 - Prob. 43PSCh. 3.6 - Prob. 44PSCh. 3.6 - Prob. 45PSCh. 3.6 - Prob. 46PSCh. 3.6 - Prob. 47PSCh. 3.6 - Prob. 48PSCh. 3.6 - Prob. 49PSCh. 3.6 - Prob. 50PSCh. 3.6 - Prob. 51PSCh. 3.6 - Prob. 52PSCh. 3.6 - Prob. 53PSCh. 3.6 - Prob. 54PSCh. 3.6 - Prob. 55PSCh. 3.6 - Prob. 56PSCh. 3.6 - Prob. 57PSCh. 3.6 - Prob. 58PSCh. 3.6 - Prob. 59PSCh. 3.6 - Prob. 60PSCh. 3.7 - Prob. 1PSCh. 3.7 - Prob. 2PSCh. 3.7 - Prob. 3PSCh. 3.7 - Prob. 4PSCh. 3.7 - Prob. 5PSCh. 3.7 - Prob. 6PSCh. 3.7 - Prob. 7PSCh. 3.7 - Prob. 8PSCh. 3.7 - Prob. 9PSCh. 3.7 - Prob. 10PSCh. 3.7 - Prob. 11PSCh. 3.7 - Prob. 12PSCh. 3.7 - Prob. 13PSCh. 3.7 - Prob. 14PSCh. 3.7 - Prob. 15PSCh. 3.7 - Prob. 16PSCh. 3.7 - Prob. 17PSCh. 3.7 - Prob. 18PSCh. 3.7 - Prob. 19PSCh. 3.7 - Prob. 20PSCh. 3.7 - Prob. 21PSCh. 3.7 - Prob. 22PSCh. 3.7 - Prob. 23PSCh. 3.7 - Prob. 24PSCh. 3.7 - Prob. 25PSCh. 3.7 - Prob. 26PSCh. 3.7 - Prob. 27PSCh. 3.7 - Prob. 28PSCh. 3.7 - Prob. 29PSCh. 3.7 - Prob. 30PSCh. 3.7 - Prob. 31PSCh. 3.7 - Prob. 32PSCh. 3.7 - Prob. 33PSCh. 3.7 - Prob. 34PSCh. 3.7 - Prob. 35PSCh. 3.7 - Prob. 36PSCh. 3.7 - Prob. 37PSCh. 3.7 - Prob. 38PSCh. 3.7 - Prob. 39PSCh. 3.7 - Prob. 40PSCh. 3.7 - Prob. 41PSCh. 3.7 - Prob. 42PSCh. 3.7 - Prob. 43PSCh. 3.7 - Prob. 44PSCh. 3.7 - Prob. 45PSCh. 3.7 - Prob. 46PSCh. 3.7 - Prob. 47PSCh. 3.7 - Prob. 48PSCh. 3.7 - Prob. 49PSCh. 3.7 - Prob. 50PSCh. 3.7 - Prob. 51PSCh. 3.7 - Prob. 52PSCh. 3.7 - Prob. 53PSCh. 3.7 - Prob. 54PSCh. 3.7 - Prob. 55PSCh. 3.7 - Prob. 56PSCh. 3.7 - Prob. 57PSCh. 3.7 - Prob. 58PSCh. 3.7 - Prob. 59PSCh. 3.7 - Prob. 60PSCh. 3.8 - Prob. 1PSCh. 3.8 - Prob. 2PSCh. 3.8 - Prob. 3PSCh. 3.8 - Prob. 4PSCh. 3.8 - Prob. 5PSCh. 3.8 - Prob. 6PSCh. 3.8 - Prob. 7PSCh. 3.8 - Prob. 8PSCh. 3.8 - Prob. 9PSCh. 3.8 - Prob. 10PSCh. 3.8 - Prob. 11PSCh. 3.8 - Prob. 12PSCh. 3.8 - Prob. 13PSCh. 3.8 - Prob. 14PSCh. 3.8 - Prob. 15PSCh. 3.8 - Prob. 16PSCh. 3.8 - Prob. 17PSCh. 3.8 - Prob. 18PSCh. 3.8 - Prob. 19PSCh. 3.8 - Prob. 20PSCh. 3.8 - Prob. 21PSCh. 3.8 - Prob. 22PSCh. 3.8 - Prob. 23PSCh. 3.8 - Prob. 24PSCh. 3.8 - Prob. 25PSCh. 3.8 - Prob. 26PSCh. 3.8 - Prob. 27PSCh. 3.8 - Prob. 28PSCh. 3.8 - Prob. 29PSCh. 3.8 - Prob. 30PSCh. 3.8 - Prob. 31PSCh. 3.8 - Prob. 32PSCh. 3.8 - Prob. 33PSCh. 3.8 - Prob. 34PSCh. 3.8 - Prob. 35PSCh. 3.8 - Prob. 36PSCh. 3.8 - Prob. 37PSCh. 3.8 - Prob. 38PSCh. 3.8 - Prob. 39PSCh. 3.8 - Prob. 40PSCh. 3.8 - Prob. 41PSCh. 3.8 - Prob. 42PSCh. 3.8 - Prob. 43PSCh. 3.8 - Prob. 44PSCh. 3.8 - Prob. 45PSCh. 3.8 - Prob. 46PSCh. 3.8 - Prob. 47PSCh. 3.8 - Prob. 48PSCh. 3.8 - Prob. 49PSCh. 3.8 - Prob. 50PSCh. 3.8 - Prob. 51PSCh. 3.8 - Prob. 52PSCh. 3.8 - Prob. 53PSCh. 3.8 - Prob. 55PSCh. 3.8 - Prob. 56PSCh. 3.8 - Prob. 57PSCh. 3.8 - Prob. 58PSCh. 3.8 - Prob. 59PSCh. 3.8 - Prob. 60PSCh. 3 - Prob. 1PECh. 3 - Prob. 2PECh. 3 - Prob. 3PECh. 3 - Prob. 4PECh. 3 - Prob. 5PECh. 3 - Prob. 6PECh. 3 - Prob. 7PECh. 3 - Prob. 8PECh. 3 - Prob. 9PECh. 3 - Prob. 10PECh. 3 - Prob. 11PECh. 3 - Prob. 12PECh. 3 - Prob. 13PECh. 3 - Prob. 14PECh. 3 - Prob. 15PECh. 3 - Prob. 16PECh. 3 - Prob. 17PECh. 3 - Prob. 18PECh. 3 - Prob. 19PECh. 3 - Prob. 20PECh. 3 - Prob. 21PECh. 3 - Prob. 22PECh. 3 - Prob. 23PECh. 3 - Prob. 24PECh. 3 - Prob. 25PECh. 3 - Prob. 26PECh. 3 - Prob. 27PECh. 3 - Prob. 28PECh. 3 - Prob. 29PECh. 3 - Prob. 30PECh. 3 - Prob. 1SPCh. 3 - Prob. 2SPCh. 3 - Prob. 3SPCh. 3 - Prob. 4SPCh. 3 - Prob. 5SPCh. 3 - Prob. 6SPCh. 3 - Prob. 7SPCh. 3 - Prob. 8SPCh. 3 - Prob. 9SPCh. 3 - Prob. 10SPCh. 3 - Prob. 11SPCh. 3 - Prob. 12SPCh. 3 - Prob. 13SPCh. 3 - Prob. 14SPCh. 3 - Prob. 15SPCh. 3 - 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