Vault Of Euclid

Average Rate of Change of a Circular Path

Multivariable calculus warmup

Let \(\vec{r}(t) = \langle \cos\left(\frac{\pi}{2} t\right), \sin\left(\frac{\pi}{2} t\right) \rangle\) as in Example 11.1.5. Find the average rate of change of \(\vec{r}(t)\) on \([-1, 1]\) and on \([-1, 5]\).
vector-valued-functionsaverage-rate-of-changedisplacementkinematicscalculus-iiimultivariable-calculusparametric-equationstrigonometric-functionsperiodicityevaluate-rate

The solution and a full step-by-step explanation are here. Sign in to read them.

What you need first

What this problem tests

Tests the ability to apply the average rate of change formula to vector-valued functions and evaluate trigonometric functions.

This problem introduces the concept of average rate of change for vector-valued functions, typically found in a Multivariable Calculus or Calculus III course.

More on Multivariable calculus