Practice Sensitivity in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
In the context of functions, sensitivity measures how much the output changes in response to a small change in the input — high sensitivity means small input changes cause large output changes.
A sensitive scale notices tiny weight differences. An insensitive one doesn't.
Example 1
easyCompute the sensitivity \Delta F / \Delta x for F(x) = 3x^2 at x = 5 with perturbation \Delta x = 0.1.
Example 2
hardA function F(x)=e^x is highly sensitive near large x. Compare the sensitivity at x=0 and x=5 using a perturbation of \Delta x=0.01.
Example 3
easyFor f(x)=10x, compute the sensitivity at x=3 with \Delta x=0.5 and compare to \Delta x=0.1.
Example 4
mediumA weather model uses T(P)=0.1P^2 where P is pressure. If P=10 and measurement error is \Delta P=\pm0.5, estimate the resulting error in T.