\( \int \int _ { R } ( 3 x + 4 y ^ { 2 } ) d A \)

D': dyferent \( f(x)=\frac{3 x^{2}+2 x}{4 x^{2}+2 x} \)

Find the area under the curve defined by \( f(x) = 2x + 1 \) between the points \( x = 1 \) and \( x = 3 \).

1. Obtenga la derivada de cada función, usando la fórmula: \( \begin{aligned} f(x)=x^{2}\end{aligned} \) \( \begin{aligned}\text { [Res. }] f(x) & =\lim _{x \rightarrow-5} \frac{(x+h)^{2}-x^{2}}{h} \\ & =\lim _{x \rightarrow 0} \frac{2 x h+h^{2}}{h} \\ & =\lim _{x \rightarrow 0}(2 x+h) \\ & =2 x\end{aligned} \) (1) \( f(x)=2 x^{2} \) \( f(x)-5 i m \)

40. Let \( f(x)=x^{3}-12 x+1 \) be defined on \( [0,3] \). What is the range of \( f \) ? \( \begin{array}{llll}\text { A. }(-\infty, \infty) & \text { B. }(-\infty, 1] & \text { C. }[-15,1] & \text { D. }[-15,17]\end{array} \)

\( y=\frac{2 x-\pi}{x \operatorname{ctg} x} \) funksiyani \( x=0 \) va \( x=\frac{\pi}{2} \) nuqtalarda uzluksizlikga tekshiring va uzilish turini aniqlang.