There is a mark indicating when the glass is filled to {{MATH_379}} ml at {{MATH_380}} cm from the base of the glass. If the glass is filled within {{MATH_381}} millimeters of the mark, what are the bounds on the volume? {{COMMENT_382}} {{COMMENT_383}} {{CMD_384}} We want to know what a small change in the height, {{MATH_385}}, does to the volume {{MATH_386}}. These small changes can be modeled by the differentials {{MATH_387}} and {{MATH_388}}. Since {{MATH_389}} and {{MATH_390}} we use the fact that {{MATH_391}} with {{MATH_392}} to see {{MATH_393}} Hence the volume will vary by roughly {{MATH_394}} milliliters. {{CMD_395}} {{CMD_396}}