\( \int_{0}^{a} \frac{1}{1+4 x^{2}}=\frac{\pi}{8} \), find \( a \)

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

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

If \( f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} \), for which values of \( x \) is \( \begin{array}{ll}1.2 .2 & f(x) \text { non real. } \\ 1.2 .3 & f(x) \text { undefined } \\ 1.2 .4 & f(x)>0\end{array} \)

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

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