Find the area under the given curve over the indicated interval. \( y=e^{2 x} ;[0,5] \) The area is \( \square \). (Round to three decimal places as needed.)

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

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

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

\( f ( x ) = \left\{ \begin{array} { l l } { \sin x } & { ; x < r } \\ { m x + b ; } & { x \geq r } \end{array} \right. \)

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