Answer:
To estimate the relative error in the area of the equilateral triangle using differentials, we can use the formula for the relative error in a function. In this case, the function is the area of the equilateral triangle.
The formula for the relative error in a function is:
Relative error = (Absolute error in the input / Value of the input) * (Derivative of the function with respect to the input)
In this case, the input is the side length of the equilateral triangle, which has an absolute error of 0.1 cm. The value of the input is 3 cm.
The derivative of the function for the area of an equilateral triangle with respect to the side length can be calculated as:
dA/ds = (√3 / 4) * s
where s is the side length.
Now, let's calculate the relative error:
Relative error = (0.1 cm / 3 cm) * [(√3 / 4) * 3 cm]
Relative error = (0.0333) * (0.433)
Therefore, the relative error in the area of the equilateral triangle is approximately 0.0144, or 1.44%.
Step-by-step explanation: