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No, vital capacity is the maximum volume a person can exhale after taking the deepest breath that they can
A mathematician is a person who enjoys doing math (and is often one who does so professionally in some capacity).
No. IQ, or intelligence quotient, is not a measure of someone's knowledge. It is a measure of a person's capacity to learn. Whether the person uses that capacity is up to them. IQ is essentially determined at birth, and so does not shift by more than a few points over the course of a lifetime.
The volume not included in the vital capacity is the residual volume (RV). Residual volume is the amount of air that remains in the lungs after a maximal exhalation and cannot be voluntarily expelled. Vital capacity, which consists of tidal volume, inspiratory reserve volume, and expiratory reserve volume, measures the maximum amount of air a person can exhale after a deep breath, excluding the residual volume.