Set up the definite integral required to find the area of the region between the graph of \( y=13-x^{2} \) and \( y=24 x+148 \) over the interval \( -5 \leq x \leq 3 \).

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

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 \( f(x)=1000 \)

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

Calcule \( \int \frac{x^{4} - 5x^{2} + 6}{x-2} \,dx \) aplicando o método de divisão longa.

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