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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

According to the model we used to solve Example 2, what happens as the top of the ladder approaches the ground? Is the model appropriate for small values of y?

To determine

To find:

Whathappens as the top of the ladder approaches the ground

Explanation

The relationship between the length of ladder and displacement along the wall and ground is given by Pythagoras theorem as l2=x2+y2 When the ladder touches the ground, the distance y is zero.

In that case, we cannot find the hypotenuse, which is the length of the ladder. Thus the relation breaks down rendering all related computations meaningless. Thus the rate of change expression we computed in example 2  no longer holds true when y is zero.

The model is not appropriate for small values of y for it results in violation of physical laws

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