(21) If \( \lim _{x \rightarrow 2} \frac{x^{2}-8 x+\mathrm{m}}{x^{2}-4}=\mathrm{k} \), then \( \mathrm{k}+\mathrm{m}= \) (a) 10 (22) If \( \lim _{x \rightarrow \mathrm{a}} \frac{x^{5}-\mathrm{a}^{5}}{x^{2}-\mathrm{a}^{2}}=20 \), then \( \mathrm{a}=\ldots \)

What is the arc length of the parametrically defined curve given by \( x(t) = t, y(t) = t^3 \) for \( t \) in the interval \([0, 2]\)?

\( y ^ { \prime \prime } + 5 y ^ { \prime } + 4 y = 3 + 8 x ^ { 2 } + 2 \cos ( 2 x ) \)

A container in the shape of an inverted cone of radius 3 metres and vertical height 4.5 metres is initially filled with liquid fertiliser. This fertiliser is released through a hole in the bottom of the container at a rate of \( 0.01 \mathrm{~m}^{3} \) per second. At time \( t \) seconds the fertiliser remaining in the container forms an inverted cone of height \( h \) metres. [The volume of a cone is \( V=\frac{1}{3} \pi r^{2} h \).] (i) Show that \( h^{2} \frac{\mathrm{~d} h}{\mathrm{~d} t}=-\frac{9}{400 \pi} \). (ii) Express \( h \) in terms of \( t \). (iii) Find the time it takes to empty the container, giving your answer to the nearest minute.

Find the derivative of the function. \( f(x)=-18 x^{\frac{3}{2}}+9 x^{1.3}+x \)

Application 3: Simplifier les expressions suivantes: \( \begin{array}{ll}A=\ln (\sqrt{3})+\ln 3-\ln 9 & ; \\ C=\ln \left(\frac{1}{3}\right)+\ln \left(\frac{3}{5}\right)+\ln \left(\frac{5}{7}\right)+\ln \left(\frac{7}{9}\right) & ;\end{array} \quad D=\ln (\sqrt[3]{2}-\ln 16 \)