\( \frac{d}{d x}\left(x^{3}+20 x+21\right) \) is (i) \( 3 x^{3}+20 \) (ii) \( 3 x^{2} \) (iii) 0 (iv) None of These

v. \( f(x)=\frac{\arcsin 3 x}{x} \)

\( f(x, y)=x^{2} y-x y^{2} \) olduğuna göre, f(-1,1) kaçtır? \( \begin{array}{lllll}\text { A) } 0 & \text { B) } 4 & \text { C) }-1 & \text { D) } 2 & \text { E) }-2\end{array} \)

If a car has an acceleration function of \( a(t) = 6t \), what is its velocity function assuming it starts from rest?

The area of a rectangular cross-section of a solid is given by the dimensions in terms of a linear function: width = \(x\) and height = \(3 - x\) for \(0 \leq x \leq 3\). Calculate the volume of the solid when these rectangles are stacked from \(x=0\) to \(x=3\).

If \( \left\langle a_{n}\right\rangle \) and \( \left\langle b_{n}\right\rangle \) are two sequences such that \( \lim _{n \rightarrow \infty} a_{n}=i, \lim _{n \rightarrow \infty} b_{n}=m \), then prove that: \( \lim _{n \rightarrow \infty}\left(a_{n}+b_{n}\right)=l+m \)