\( \begin{array} { l } { \lim _ { x \rightarrow 3 } ( \frac { x - 3 } { x ^ { 2 } - 9 } ) } \\ { x } \\ { x ( x ) } \\ { f ( x ) } \\ { - 2.99 } \end{array} - 2.999 | 3 | 3.001 | 3.01 | ) \)

Find the limit value for the following function: \[ \lim _{n \rightarrow \infty} \frac{\sqrt{n}}{\sqrt{3 n-1}} \]

\( f ( x ) = \int e ^ { 58379 } d x \)

47. (99-4 32) \( y=\pi \sin \pi x+2 x-4 \) funksiyaning \( x= \) 1 bo'ganda giymati 3 ga teng bo'ladigan bosh- lang'ich funksiynsi \( x \) ning qanday qiymatida nolga aylanadi? \( \begin{array}{llll}\text { A) } 0 & \text { B) } 1 & \text { C) } 0,5 & \text { D) } 2 \\ \text { E) }-2\end{array} \)

Check whether the differential equation: Is Exact or not? If yes, \( \frac{\text { find }}{\left(6 x^{2}+4 x y+y^{2}\right) d x+\left(2 x^{2}+2 x y-3 y^{2}\right) d y=0} \).

2. Calcolare l'integrale della funzione \( f(x, y)=x+2 y \) sul settore circolare \[ S=\left\{(x, y):(x+1)^{2}+y^{2} \leq 2, y \leq 0, y \leq-x-1\right\} \]