A rate limiter emits $a_n=\dfrac{n}{n+1}$ at step $n$. What is $\lim_{n\to\infty} a_n$? (CO1)

A stabilizer aggregates the series $\displaystyle \sum_{n=1}^{\infty} \tfrac{1}{n^{2}}$ as a variance estimate. How does this series behave? (CO2)

An image‑intensity model is $L(x,y)=x^{4}-2x^{2}y^{2}+y^{4}$. Compute $H=x^{2}L_{xx}+2xy\,L_{xy}+y^{2}L_{yy}$ at $(2,1)$. (CO4)

Consider the series $\displaystyle \sum_{n=1}^{\infty} \tfrac{2^{n}}{n!}$. What does D’Alembert’s ratio test conclude? (CO3)

Consider the alternating series $\displaystyle \sum_{n=1}^{\infty} (-1)^{n} \tfrac{1}{n^{2}}$. Which classification is correct? (CO3)

Which of the following series is divergent? (CO4)

Determine the radius of convergence of the power series $\displaystyle \sum_{n=1}^{\infty} \tfrac{x^{n}}{n}$. (CO4)

Let $z=xy^{2}$. Evaluate $\dfrac{\partial z}{\partial y}$ at $(1,2)$. (CO1)

Let $f(x,y)=x^{2}y+y^{3}$. Evaluate $x f_{x}+y f_{y}$. (CO2)

For $u=x^{2}+y^{2}$ and $v=x^{2}-y^{2}$, compute the Jacobian $\dfrac{\partial(u,v)}{\partial(x,y)}$. (CO5/CO6)