Given the following revenue and cost functions, find the \( x \)-value that makes profit a maximum. Round answer to nearest hundredth. (Recall that profit equals revenue minus cost.) \( R(x)=58 x-2 x^{2} ; C(x)=22 x+96 \) A. 18.00 B. 10.00 C. 9.00 D. 14.50

11. Find the values of \( a \) and \( b \) that make \( f \) continuous everywhere. \[ f(x)=\left\{\begin{array}{ll}\frac{x^{2}-4}{x-2} & \text { if } x<2 \\ a x^{2}-b x+3 & \text { if } 2 \leq x<3 \\ 2 x-a+b & \text { if } x \geq 3\end{array}\right. \]

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

Show that \( F(x)=|x| \) is continuous everywhere.

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

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