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Identifying a Parametric Surface as a Cone

Multivariable calculus warmup

Describe the surface parameterized by \( \mathbf{r}(u, v) = \langle u \cos v, u \sin v, u \rangle \), \( -\infty < u < \infty \), \( 0 \le v < 2\pi \).
parametric-surfacesmultivariable-calculusconecartesian-coordinatesparameter-eliminationpythagorean-identitytrigonometric-functionsquadric-surfacesidentify-surface

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What this problem tests

Tests the ability to convert between parametric and Cartesian representations of surfaces.

This problem is typical in a multivariable calculus course when introducing parametric surfaces and surface integrals.

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