# Math Help - Differentials

1. ## Differentials

Two questions that are giving me trouble; could someone please show me how?

Question One

A mushroom was observed while growing, and all linear dimensions were growing proportionately. Therefore, the volume increased according to the formula $V=cL^3$ Where L is any linear dimension and c is a constant. Show that

$
\frac{1} {V}\left[\frac{dv} {dt}\right] = 3 \frac{1}{L}\left[\frac{dL}{dt}\right]
$

Using differentials find the percentage error in g is l is measured accurately but T has an error of 1%

Question Two

The acceleration due to gravity g can be determined by measuring the period of swing of a pendulum. If the length of the pendulum is l and the measured period is T, then g is given by the formula

$g = \frac{4 (pi)^2l} {T^2}$