Mini Exam 6 — Timed Mini Exams

Questions in this quiz (10)

1. A water tank $$12$$ feet high is mounted against a wall. The back is in the shape of the parabola $$y=x^2$$ and all cross sections parallel to the floor are squares. If water is being poured in at a rate of $$8$$ $$ft^3/hr$$, how fast, in $$ft/hr$$, is the water level rising when it is $$4$$ feet deep?

   • $$1\frac{1}{8}$$
   • $$1\frac{1}{4}$$
   • $$1\frac{1}{2}$$
   • $$1$$

2. If $$\cos(xy)=x$$ then $$\frac{dy}{dx}=?$$

   • $$\frac{-1-y\sin(xy)}{x\sin(xy)}$$
   • $$\frac{y\sin(xy)-1}{x\sin(xy)}$$
   • $$\frac{1-y\sin(xy)}{x\sin(xy)}$$
   • $$\frac{y\sin(xy)}{1-x\sin(xy)}$$

3. Let $$x$$>$$0$$. Suppose $$\frac{d}{dx}f(x)=g(x)$$ and $$\frac{d}{dx}g(x)=f(\sqrt{x})$$ then $$\frac{d^2}{dx^2}f(x^2)=$$?

   • $$2g(x^2)$$
   • $$2xg(x^2)$$
   • $$2g(x^2)+4x^2f(x)$$
   • $$2g(x^2)+4x^2f(\sqrt{x})$$

4. An object moving along a line has acceleration $$a(t)=2t+\frac{1}{1+t^{2}}$$ and is at rest when $$t=0$$. Its average velocity from $$t=0$$ to $$t=2$$ is:

   • $$A.$$ $$1.48$$
   • $$2.04$$
   • $$2.67$$
   • $$3.05$$

5. Water is poured into a conical tank at a constant rate. If $$W(t)$$ is the rate of increase of the depth of the water, then $$W$$ is:

   • linear and increasing
   • linear and decreasing
   • concave up
   • concave down

6. The graph of $$f'$$ is shown above. If $$f(7)=3$$ then $$f(1)=$$?

   • $$-10$$
   • $$-4$$
   • $$10$$
   • $$16$$

7. If a block of ice melts at the rate$$M(t)=\frac{60}{t+3}$$ $$cm^3/min$$, how much ice melts during the first $$4$$ minutes?

   • $$20$$ $$cm^3$$
   • $$30$$ $$cm^3$$
   • $$36$$ $$cm^3$$
   • $$60\ln\frac{7}{3}$$ $$cm^3$$

8. The length of the curve $$y=e^x$$ between $$(0,1)$$ and $$(1,e)$$ is:

   • $$1.317$$
   • $$1.543$$
   • $$1.718$$
   • $$2.003$$

9. $$\lim_{h\to 0}\frac{\tan\left(\frac{\pi}{4}+h\right)-1}{h}=$$?

   • $$0$$
   • $$\frac{1}{2}$$
   • $$1$$
   • $$2$$

10. The region $$S$$ is bounded by $$y=\sec x$$ and $$y=2$$ on the interval where they intersect. What is the volume of the solid formed when $$S$$ is rotated about the $$x$$-axis?

    • $$6.28$$
    • $$15.44$$
    • $$18.85$$
    • $$25.13$$