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Q 1/10
Score 0
300
Q 2/10
Score 0
Each hour the load grows by $25\%$ from $L_0$. Total over first $n$ hours equals
300
$L_0\,(1.25)^{n}$
$L_0\,(1-1.25^{n})$
$L_0\,\dfrac{1.25^{n}-1}{1.25-1}$
$L_0\,n$
10 questions
Q.
1
300 sec
Q.
Each hour the load grows by $25\%$ from $L_0$. Total over first $n$ hours equals
2
300 sec
Q.
Telemetry for a device is modeled by $z(x,y)=x^2+2xy$. The coordinates depend on time $t$ by $x(t)=1+t$ and $y(t)=2-t$. Find $\dfrac{dz}{dt}$.
3
300 sec
Q.
For $u=2x-y$ and $v=x+3y$, the value of $\dfrac{\partial(x,y)}{\partial(u,v)}$ equals
4
300 sec
Q.
In an AP with $a=11$ and $d=9$, the smallest $n$ with $a_n>200$ equals
5
300 sec
Q.
Sum of GP with $a=7$, $r=\tfrac{1}{3}$ for $n=6$ equals
6
300 sec
Q.
For $u=5x+y$ and $v=-x+4y$, compute $\dfrac{\partial(u,v)}{\partial(x,y)}$
7
300 sec
Q.
Using linearization at $(0,0)$, approximate $f(x,y)=\ln(1+x+y)$ at $(0.1,-0.05)$
8
300 sec
Q.
In a graphics pipeline, the loss is modeled by $L(x,y)=x^{4}-2x^{2}y^{2}+y^{4}$. Define $H(x,y)=x^{2}L_{xx}+2xy\,L_{xy}+y^{2}L_{yy}$. Evaluate $H(2,1)$.
