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Q 1/10
Score 0
A telemetry stream reports $a_n=\tfrac{1}{n}$ at the $n$-th second. The system labels a sequence as "well‑behaved" if it is both bounded and monotone. Which assessment best describes $(a_n)$? (CO1)
300
Increasing and unbounded
Oscillatory without bound
Divergent and increasing
Decreasing and bounded
Q 2/10
Score 0
A drone’s altitude is modeled by $z(x,y)=x^{2}+2xy$ with $x(t)=1+t$ and $y(t)=2-t$. Compute $\dfrac{dz}{dt}$ at $t=0$. (CO2)
300
$5$
$0$
$4$
$2$
10 questions
Q.
A telemetry stream reports $a_n=\tfrac{1}{n}$ at the $n$-th second. The system labels a sequence as "well‑behaved" if it is both bounded and monotone. Which assessment best describes $(a_n)$? (CO1)
1
300 sec
Q.
A drone’s altitude is modeled by $z(x,y)=x^{2}+2xy$ with $x(t)=1+t$ and $y(t)=2-t$. Compute $\dfrac{dz}{dt}$ at $t=0$. (CO2)
2
300 sec
Q.
A coordinate remap uses $u=2x-y$ and $v=x+3y$. Evaluate the inverse Jacobian $\dfrac{\partial(x,y)}{\partial(u,v)}$. (CO5/CO6)
3
300 sec
Q.
Consider the harmonic series $\displaystyle \sum_{n=1}^{\infty} \tfrac{1}{n}$. Which statement best describes its behavior? (CO2)
4
300 sec
Q.
Consider the series $\displaystyle \sum_{n=1}^{\infty} \tfrac{n}{2^{n}}$. What does D’Alembert’s ratio test conclude? (CO3)
5
300 sec
Q.
Consider the alternating series $\displaystyle \sum_{n=1}^{\infty} \tfrac{(-1)^{n}}{n}$. Which classification is correct? (CO3)
6
300 sec
Q.
Which of the following series is conditionally convergent? (CO4)
7
300 sec
Q.
Determine the radius of convergence of the power series $\displaystyle \sum_{n=0}^{\infty} \tfrac{x^{n}}{n!}$. (CO4)
8
300 sec
Q.
Let $f(x,y)=x^{3}+y^{3}$. Evaluate $x f_{x}+y f_{y}$. (CO2)
9
300 sec
Q.
Let $S(x,y)=x^{3}+3x^{2}y+y^{3}$. Compute $x^{2}S_{xx}+2xy\,S_{xy}+y^{2}S_{yy}$ at $(1,2)$. (CO4)
