The enclosed area of the graph of the function \( y=\left[x^{2}\right] \) and \( x \)-ares \( x=-2+0 x=2 \) which is? \( 10-4(\sqrt{2}+\sqrt{2}) \) \( 10-5(\sqrt{5}+\sqrt{2}) \) \( 10-2(\sqrt{3}+\sqrt{2}) \) \( 10-8(\sqrt{2}+\sqrt{3}) \)

Given \( \mathrm{TP}=90 \mathrm{~K}^{2}-\mathrm{K}^{3} \) find a. Marginal product b. Average product c. The value of output which equates average product and marginal product

3. Given \( T P=90 \mathrm{~K}^{2}-\mathrm{K}^{3} \) find a. Marginal product b. Average product c. The value of output which equates average product and marginal product

c. The value of output which equates average product and marginal product Use the product rule to find the first-order partials for each of the following functions a. \( z=3 x^{2}(5 x+7 y) \) b. \( z=(9 x-4 y)(12 x+2 y) \)

A particle \( P \) moves in a straight line so that, \( t \) seconds after passing a fixed point \( O \), its displacement, \( s \) metres, is given by \( s=4 t^{3}-15 t^{2}+18 t \). Find (i) the velocity of \( P \) when \( t=3 \), (ii) the acceleration of \( P \) when \( t=3 \), (iii) the values of \( t \) when \( P \) is at instantaneous rest, (iv) the distance travelled by \( P \) in the first 2 seconds of its motion, (v) the distance of \( P \) from \( O \) when \( t=2 \).

Identify the horizontal asymptote of the function \( f(x) = 3 e^{-x} + 5 \).