Use the Lagrange-multiplier method to lind the stationary vatues of \( z \) : (a) \( z=x y \), subject to \( x+2 y=2 \).

(c) \( \int_{6}^{0}(2+5 x) e^{\frac{1}{3} x} d x \)

(b) Solve the following first order differential equations. i) \( \frac{d y}{d x}=4 x^{3}-8 x+7 \) kena tambah 1 ii) \( x \frac{d y}{d x}=5 x^{3}+4 \) iii) \( y^{3} \frac{d y}{d x}=\frac{e^{4 x}+4 x}{y} \)

integral \( \int_{0}^{1} \int_{e^{y}}^{e} \frac{x}{\ln x} d x d y \) (by

\( \lim _ { x \rightarrow 0 } \frac { 3 ( x - \operatorname { cts } x ) } { x } \)

June 2018 ZIMSEC Paper 1 Solve the equations: \( e^{2 x}=4 e^{2-x} \) giving the answer in exact form. November 2010 ZIMSEC Paper 1