Find \( f_{x}(3,-3) \) if \( f(x, y)=5 x^{2}+6 x y-5 y^{2}+2 x-9 y-2 \) \( f_{x}(3,-3)=\square \)

(d) \( \lim _{n \rightarrow+\infty} \frac{\operatorname{sen}(1 / n)}{\operatorname{sen}(3 / n)} \)

Find differenthal equation of the primitue \( x y+x^{2} y+y^{2}=13 \)

Solve the differential equation \( \frac{dy}{dx} = 6y \) using separation of variables.

\( \lim _ { n \rightarrow \infty } [ \frac { 1 } { \sqrt { 4 n ^ { 2 } - 1 } } + \frac { 1 } { \sqrt { 4 n ^ { 2 } - 2 ^ { 2 } } } + \cdots + \frac { 1 } { \sqrt { 3 n ^ { 2 } } } ] \)

2. \( \left\{x_{n}\right\} \) ketma-ketlikning yuqori va quyi limitlari topilsin. \( x_{n}=\left(1+\frac{1}{n}\right)^{n}(-1)^{n}+\sin \frac{n \pi}{4} \) 3. Limit hisoblansin. \( \lim \left(\sqrt{1+x+x^{2}}-\sqrt{1-x+x^{2}}\right) \)