Practice question · Match the pairs
Match each problem type to the best multivariable technique.
- Volume under a surface over a disk
- Optimize f on a circle constraint
- Flux through a closed surface
- Rate of change along a curve
- Double integral in polar coordinates
- Divergence theorem
- Chain rule / directional derivative
- Lagrange multipliers
Hints
- Ask what the problem asks for: an extreme value, an accumulation, or a rate.
- A constraint equation points toward one particular method.
Show the answer
- Volume under a surface over a disk → Double integral in polar coordinates
- Optimize f on a circle constraint → Lagrange multipliers
- Flux through a closed surface → Divergence theorem
- Rate of change along a curve → Chain rule / directional derivative
Why
Choosing the right technique is the key skill in problem-solving.
Practise Problem-Solving: Multivariable Calculus
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