Find the absolute extrema if they exist, as well as all values of \( x \) where they occur, for the function \( f(x)=\frac{5+x}{8-x} \) on the domain [ \( -8,0 \) ].

Solve the following first order differential equations. \( \frac{d y}{d x}=4 x^{3}-8 x+7 \) bena tambah \( x \frac{d y}{d x}=5 x^{3}+4 \)

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

By using Newton-Raphson Method, determine the root for \( x^{3}+2 x^{2}-1=0 \). Given \( x_{0}=0.5 \). Give the answer correct to four decimal places. Dengan mengomenan

(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) \( y^{3} \frac{d y}{d x}=\frac{e^{4 x}+4 x}{y} \)

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