Sendo \( f(x, y)=3 x^{3}-6 x y+y^{2} \), assinale a alternativa que apresenta, nesta ordem, o cálculo de \( \frac{\partial f}{\partial x}(1,-2) \) e \( \frac{\partial f}{\partial y}(-3,2) \). Escolha uma opçao: a. 21 e 22 . b. 22 e 21 c. -3 e - 14 d. -3 e 22 . e. 21 e 14

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

Given that \( \int_{0}^{1}\left(2+3 \cos \frac{1}{2} x\right) d x=\int_{-1}^{2} e^{2 x+1} d x \), find the value of \( k \), giving your answer correct to 3 decimal places.

\( \int _ { - \infty } ^ { \infty } x ^ { 4 } e ^ { - x ^ { 3 } } d x \)

Find the following indefinite integral \[ \int 9 x^{2} d x \]

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