(a) Find the area of the region enclosed by: \[ y=\sin x \text {, and } y=2 \cos x, \quad \text { over the interval }[0, \pi] \] (b) Evaluate the following integral: \[ \int \frac{x^{3}}{\sqrt{1-x^{2}}} d x \]

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

8. If \( f(x)=x^{2}+10 \sin x \), show that there is a number \( c \) such that \( f(x)=1000 \).

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

7. Find \( \lim _{x \rightarrow 2} \frac{\sqrt{6-x}-2}{\sqrt{3-x}-1} \) 8. If \( f(x)=x^{2}+10 \sin x \), show that there is a number \( c \) such that \( f(x)=1000 \)

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