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The side of a square floor tile is measured to be 16 inches, with a possible error of 1/32 inch. Use differentials to approximate the possible error and the relative error in computing the area of the square. Step 1 Recall that the formula for the area of a square is A = x We are given that the side of the square floor tile is x = 16 inches and the possible error is 1 32 Step 2 Ax= dx = ± To approximate the possible propagated error in computing the area of the square, differentiate A = x² with respect to x. dA dx = where x is the side of the square. dA = x dx

The side of a square floor tile is measured to be 16 inches, with a possible error of 1/32 inch. Use differentials to approximate the possible error and the relative error in computing the area of the square. Step 1 Recall that the formula for the area of a square is A = x We are given that the side of the square floor tile is x = 16 inches and the possible error is 1 32 Step 2 Ax= dx = ± To approximate the possible propagated error in computing the area of the square, differentiate A = x² with respect to x. dA dx = where x is the side of the square. dA = x dx

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Title: Error Approximation Using Differentials** **Introduction:** The side of a square floor tile is measured to be 16 inches, with a possible error of 1/32 inch. Use differentials to approximate the possible error and the relative error in computing the area of the square. --- **Step 1:** Recall that the formula for the area of a square is \( A = x^2 \), where \( x \) is the side of the square. We are given that the side of the square floor tile is \( x = 16 \) inches and the possible error is \[ \Delta x = dx = \pm \frac{1}{32}. \] --- **Step 2:** To approximate the possible propagated error in computing the area of the square, differentiate \( A = x^2 \) with respect to \( x \). \[ \frac{dA}{dx} = \_\_\_ \cdot x \] \[ dA = \_\_\_ \cdot dx \] --- **Instructions:** - Enter the derivative value in the text boxes provided. - Click "Submit" once you have completed your calculations. **Note:** Use this method to calculate the possible error (propagated and relative) in the area of the square to ensure precision in your measurements. **Submit | Skip (you cannot come back)** **Conclusion:** Understanding and applying differentials allows us to handle measurement errors and their effects on calculations in practical scenarios.
Transcribed Image Text:**Title: Error Approximation Using Differentials** **Introduction:** The side of a square floor tile is measured to be 16 inches, with a possible error of 1/32 inch. Use differentials to approximate the possible error and the relative error in computing the area of the square. --- **Step 1:** Recall that the formula for the area of a square is \( A = x^2 \), where \( x \) is the side of the square. We are given that the side of the square floor tile is \( x = 16 \) inches and the possible error is \[ \Delta x = dx = \pm \frac{1}{32}. \] --- **Step 2:** To approximate the possible propagated error in computing the area of the square, differentiate \( A = x^2 \) with respect to \( x \). \[ \frac{dA}{dx} = \_\_\_ \cdot x \] \[ dA = \_\_\_ \cdot dx \] --- **Instructions:** - Enter the derivative value in the text boxes provided. - Click "Submit" once you have completed your calculations. **Note:** Use this method to calculate the possible error (propagated and relative) in the area of the square to ensure precision in your measurements. **Submit | Skip (you cannot come back)** **Conclusion:** Understanding and applying differentials allows us to handle measurement errors and their effects on calculations in practical scenarios.
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