Final answer:
Estimating the maximum error using differentials is a concept from differential calculus, used to approximate how small changes in variables influence functions. The correct context would be Multivariable Calculus. Measuring changes in average rainfall is less related to vector calculus than other options.
Step-by-step explanation:
To estimate the maximum error in a problem using differentials, one would typically employ calculus, specifically differential calculus. This subject focuses on understanding how small changes in variables can affect the overall outcome of functions.
Estimations are made using the derivative of a function, which provides the rate of change. When you are looking to approximate the error in some measurement, differential calculus techniques such as linear approximation or the use of a differential might be used.
Hence, among the provided options, the most appropriate context for using differentials to estimate maximum error is,
- Integral Calculus
- Differential Equations
- Multivariable Calculus
As for the unrelated question: Which method is not an application of vector calculus? The option d) To measure changes in average rainfall might be considered less directly related to vector calculus as it is generally an analysis of scalar quantities over time rather than vector fields.