Error Calculation and Function Analysis

The video tutorial explains how to use linear approximation to estimate the change in Y (delta Y) for the function Y = sine 3X, given delta X = 0.2 at X = 0. It uses a tangent line at X = 0 for approximation and demonstrates the process through graphical representation. The tutorial covers calculating the derivative of the function, finding differential Y, and estimating delta Y. It concludes with calculating the error percentage between the estimated and true change in Y, providing a comprehensive understanding of linear approximation and error analysis.

What is the initial function given in the problem?

• Y = 3X

• Y = sin(3X)

• Y = cos(3X)

• Y = tan(3X)

What is the purpose of using a tangent line in this problem?

• To find the exact value of Y

• To determine the maximum value of the function

• To approximate the change in Y

• To calculate the integral of the function

In the graph explanation, what color is used to represent the tangent line?

• Yellow

• Red

• Green

• Blue

What is the derivative of the function Y = sin(3X)?

• 3 * cos(3X)

• 3 * sin(3X)

• sin(3X)

• cos(3X)

What is the value of differential X (DX) in this problem?

• 0.3

• 0.2

• 0.1

• 0.4

How is the error percentage calculated in this context?

• (Delta Y - Differential Y) / Differential Y * 100

• (Differential Y - Delta Y) / Delta Y * 100

• (Differential Y + Delta Y) / Delta Y * 100

• (Differential Y * Delta Y) / 100

What is the true change in Y (Delta Y) when X changes from 0 to 0.2?

• tan(0.6)

• cos(0.6)

• sin(0.6)

• 0.6

What is the approximate error percentage calculated in the video?

• 6.26%

• 8.26%

• 5.26%

• 7.26%

What mathematical operation is used to convert the error to a percentage?

• Subtraction

• Addition

• Multiplication

• Division

What is the final step in calculating the error percentage?

• Rounding the result to two decimal places

• Subtracting the true change from the estimate

• Dividing the estimate by the true change

• Multiplying the result by 10