\( \frac{d}{dx}(x\times \sin (xy-y^{2})=x^{2}-1) \)

41) \( \lim _{x \rightarrow \pi}\left(x^{2}-\pi^{2}\right) \tan \frac{x}{2} \)

53) \( \lim _{x \rightarrow \frac{\pi}{3}} \frac{2 \cos x-1}{\sqrt{3}-\tan x} \)

If a fo \( f(x) \) sefinet beloe is contincious at \( x=0 \) Find the volue of \( k \). \( f(x)=\left\{\begin{array}{l}\frac{1-\cos 2 x}{2 x^{2}}, x<0 \\ k, x=0 \\ \frac{x}{|x|}, x>0 .\end{array}\right. \)

Find the directional derivative of \( \phi x, y, z=x^{2} y z+4 x z^{2} \) at the point \( (1,-2-1) \) in the direction \( 2 i-j-2 k \) Select one: \( \frac{17}{3} \) \( \frac{33}{3} \) \( \frac{37}{3} \) \( \frac{7}{3} \)

1. Find the fourior series of the fanction \( f(x)=\left\{\begin{array}{ll}-1 ; & -1<x<0 \\ 1 ; & 0<x<1\end{array}\right. \)