Use differentials to estimate the error

In summary, differentials are useful for estimating error in a function by approximating the change in the function based on small changes in the input variable. The formula for calculating error using differentials is dy = f'(x) * dx, where dy is the change in the output variable, f'(x) is the derivative of the function, and dx is the change in the input variable. This method can be used for any differentiable function, but the accuracy of the estimate depends on the size of the input variable and the smoothness of the function. However, there are limitations to using differentials for error estimation, as it assumes differentiability and small changes in the input variable and may not be accurate for functions with high variability or sharp
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One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30°, with a possible error of ±1°.
(a) Use differentials to estimate the error in computing the length of the hypotenuse. (Round your answer to two decimal places.)
±...cm(b) What is the percentage error? (Round your answer to the nearest integer.)
±... %
 
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FAQ: Use differentials to estimate the error

How do differentials help in estimating error?

Using differentials, we can approximate the change in a function based on small changes in the input variable. This can help us estimate the error in a function by comparing it to the actual value.

What is the formula for calculating error using differentials?

The formula for calculating error using differentials is given by: error = dy = f'(x) * dx, where dy is the change in the output variable, f'(x) is the derivative of the function, and dx is the change in the input variable.

Can differentials be used to estimate errors in any type of function?

Yes, differentials can be used to estimate errors in any type of function, as long as the function is differentiable.

How accurate are the error estimates obtained using differentials?

The accuracy of the error estimates obtained using differentials depends on the size of the input variable and the function itself. Generally, the smaller the input variable and the smoother the function, the more accurate the estimate will be.

Are there any limitations to using differentials for error estimation?

Yes, there are limitations to using differentials for error estimation. This method assumes that the function is differentiable and that the change in the input variable is small. Additionally, it may not be accurate for functions with high variability or sharp changes.

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