¿De \( \int \frac{x+1}{(x-2)(x-3)(x-1)} d x \) cuál es el planteamiento de las fracciones parciales? a. No es posible plantear fracciones para el proceso de la solución de la integral b. \( \frac{A}{(x-1)}+\frac{B}{(x-2)}-\frac{C}{(x-3)} \) - c. \( \frac{A}{(x-1)}+\frac{B}{(x-2)}+\frac{C}{(x+3)} \) - d. \( \frac{A}{(x-1)}+\frac{B}{(x-2)}+\frac{C}{(x-3)} \) O e. \( \frac{A}{(x-1)}+\frac{B}{(x+2)}+\frac{C}{(x-3)} \)

2. The rate of certain chemical reaction is given by \( r(x)=k x(a-x) \), \( 0 \leq x \leq a, a>0 \) and \( k>0 \). For what values of \( x \) does the rate of reaction increase? \( \begin{array}{llll}\text { A. } 0 \leq x \leq \frac{a}{2} & \text { B. } \frac{a}{2} \leq x \leq a & \text { C. }-\infty \leq x \leq \frac{a}{2} & \text { D. } \frac{a}{2} \leq x \leq \frac{3 a}{4}\end{array} \)

To find the turning point and the degree of the polynomial \( P(x)=x^{99}-1 \), let's break it

et \( f(x)=x^{4}-6 x^{2}+1 \) on \( [-2,3] \). Which of the following is a local maximum val \( \begin{array}{llll}f \\ f\end{array} \) \( \begin{array}{llll}f(0) & \text { B. } f(\sqrt{3}) & \text { C. } f(3) & \text { D. } f(-\sqrt{3})\end{array} \)

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) \( f(x)=2 x^{2} \) \( f(x)-5 i m \)

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