Use a change of variables to evaluate the following definite integral. \( \int_{0}^{2} \frac{36 q}{\left(q^{2}+2\right)^{3}} d q \) \( \int_{0}^{2} \frac{36 q}{\left(q^{2}+2\right)^{3}} d q=\square \) (Type an integer or a simplified fraction.).

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

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

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

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

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