Chapter 4: Q7MP (page 238)

About how much (in percent) does an error of 1% in x and y affect $x^{3} y^{2}$ ?

Short Answer

Expert verified

The maximum value of the product of the three positive numbers is $f = \frac{1}{27}$ .

Step by step solution

Given Information

The value of $\frac{d f}{f}$ in percent is 5%.

Derivative

The process of finding the derivative of a function is termed as differentiation. The derivative of y with respect to x is given as $\frac{d y}{d x}$ .

Find the value of dff in percent.

The differentiation is:

$\frac{d x}{d x} = 1 % = \frac{1}{100} \dots (2) \frac{d y}{d y} = 1 % = \frac{1}{100} \dots (3)$

Now differentiate equation (1) as:

$d f = x^{3} d (y^{2}) + y^{2} d (x^{3}) d f = x^{3} (2 y) d y + y^{2} (3 x^{2}) d x \frac{d f}{f} = \frac{x^{3} (2 y)}{x^{3} y^{2}} d y + \frac{y^{2} (3 x^{2})}{x^{3} y^{2}} d x \frac{d f}{f} = 2 \frac{d y}{y} + 3 \frac{d x}{x}$

Solving further as:

$\frac{d f}{f} = 2 \times \frac{1}{100} + 3 \times \frac{1}{100} \frac{d f}{f} = \frac{2}{100} + \frac{3}{100} \frac{d f}{f} = \frac{5}{100} \frac{d f}{f} = 5 %$

Therefore, the answer is $\frac{d f}{f} = 5 %$ .

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About how much (in percent) does an error of 1% in x and y affect $x^{3} y^{2}$ ?

Short Answer

Step by step solution

Given Information

Derivative

Find the value of dff in percent.

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About how much (in percent) does an error of 1% in x and y affect x3y2?

Short Answer

Step by step solution

Given Information

Derivative

Find the value of dff in percent.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

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About how much (in percent) does an error of 1% in x and y affect $x^{3} y^{2}$ ?