An oil tank is to be drained for cleaning. There are {{MATH_1}} gallons of oil left in the tank {{MATH_2}} minutes after the draining began, where {{MATH_3}}. {{CMD_4}} Find the {{CMD_5}}average rate{{CMD_6}} at which oil drains during the first {{MATH_7}} minutes. {{MATH_8}} {{CMD_9}} Find the {{CMD_10}}average rate{{CMD_11}} at which oil drains during the time interval {{MATH_12}}. {{MATH_13}} {{CMD_14}} Find the {{CMD_15}}rate{{CMD_16}} at which oil is draining {{MATH_17}} minutes after the draining began. {{MATH_18}} {{CMD_19}} Find the {{CMD_20}}average rate{{CMD_21}}, {{MATH_22}}, at which oil drains during the time interval {{MATH_23}} if {{MATH_24}}. {{MATH_25}} Now find the {{CMD_26}}average rate{{CMD_27}}, {{MATH_28}}, at which oil drains during the time interval {{MATH_29}} if {{MATH_30}}. {{MATH_31}} {{CMD_32}} Using your result, compute the limit {{MATH_33}} {{CMD_34}} What does this limit {{MATH_35}} represent? {{CMD_36}} {{CMD_37}}The average rate of change at {{MATH_38}}.{{CMD_39}} {{CMD_40}}The quantity {{MATH_41}}.{{CMD_42}} {{CMD_43}}The instantaneous rate of change of {{MATH_44}} at {{MATH_45}}.{{CMD_46}} {{CMD_47}}The derivative of {{MATH_48}} at {{MATH_49}}.{{CMD_50}} {{CMD_51}} {{CMD_52}} Suppose the oil tank has been completely drained and is now being refilled. Let {{MATH_53}} denote the gallons of oil in the tank {{MATH_54}} minutes after the refilling process began. Suppose we are told that the function {{MATH_55}} is a {{CMD_56}}differentiable function{{CMD_57}} and that the tank is so large that it will take a while to fill.