Page:Calculus Made Easy.pdf/67

Find the differential coefficients of

(7) $y={\dfrac {2x+3}{3x+2}}$.	(8) $y={\dfrac {1+x+2x^{2}+3x^{3}}{1+x+2x^{2}}}$.
(9) $y={\dfrac {ax+b}{cx+d}}$.	(10) $y={\dfrac {x^{n}+a}{x^{-n}+b}}$.

(11) The temperature $t$ of the filament of an incandescent electric lamp is connected to the current passing through the lamp by the relation

$C=a+bt+ct^{2}$.

Find an expression giving the variation of the current corresponding to a variation of temperature.

(12) The following formulae have been proposed to express the relation between the electric resistance $R$ of a wire at the temperature $t^{\circ }$ C., and the resistance $R_{0}$ of that same wire at $0^{\circ }$ Centigrade, $a$, $b$, $c$ being constants.

$R=R_{0}(1+at+bt^{2})$.
$R=R_{0}(1+at+b{\sqrt {t}})$.
$R=R_{0}(1+at+bt^{2})^{-1}$.

Find the rate of variation of the resistance with regard to temperature as given by each of these formulae.

(13) The electromotive-force $E$ of a certain type of standard cell has been found to vary with the temperature t according to the relation

$E=1.4340{\bigl [}1-0.000814(t-15)+0.000007(t-15)^{2}{\bigr ]}$ volts.

Find the change of electromotive-force per degree, at $15^{\circ }$, $20^{\circ }$ and $25^{\circ }$.