Mini Exam 2 — Timed Mini Exams

Questions in this quiz (10)

1. $$\lim_{x\to1}\frac{x^2-1}{x-1=}$$?

   • $$0$$
   • $$1$$
   • $$2$$
   • $$3$$

2. Let$$f(x)=\frac{\sqrt{x+5}-3}{x-4}$$, $$x\ne4$$$$f(4)=c$$and let $$f$$ be continuous at $$x=4$$. Then $$c=$$?

   • $$\frac{1}{6}$$
   • $$\frac{1}{4}$$
   • $$\frac{1}{3}$$
   • $$\frac{1}{2}$$

3. $$\int_{0}^{\frac{\pi}{2}}\sin^2x\cos x\,dx=$$?

   • $$-1$$
   • $$\frac{1}{3}$$
   • $$\frac{2}{3}$$
   • $$1$$

4. If the displacement from the origin of a particle moving along the $$x$$-axis is given by $$s=2+(t-1)^3$$ then the number of times the particle reverses direction is:

   • $$0$$
   • $$1$$
   • $$2$$
   • $$3$$

5. If$$f(x)=x^2$$ for $$x$$<$$3$$$$f(x)=6x-x^2$$ for $$x$$>$$3$$then $$\int_{0}^{5}f(x)\,dx$$ equals:

   • $$\frac{22}{3}$$
   • $$\frac{25}{3}$$
   • $$\frac{28}{3}$$
   • $$\frac{73}{3}$$

6. If the position of a particle on a line at time $$t$$ is given by $$s=t^3-3t,$$ then the speed of the particle is decreasing when:

   • $$-1$$ < $$t$$ < $$1$$
   • $$0$$ < $$t$$ < $$1$$
   • $$t$$ < $$-1$$
   • $$t$$ > $$1$$

7. A rectangle with one side on the $$x$$-axis is inscribed in the triangle formed by the lines$$y=x,$$ $$y=0,$$ and $$x+y=8.$$The area of the largest such rectangle is:

   • $$4$$
   • $$6$$
   • $$8$$
   • $$10$$

8. The $$x$$-value of the first-quadrant point that is on the curve $$x^2-y^2=4$$ and closest to the point $$(2,0)$$ is:

   • $$1$$
   • $$\sqrt{2}$$
   • $$2$$
   • $$3$$

9. If $$y=\ln(5x+2)$$ then $$\frac{d^2y}{dx^2}$$ is:

   • $$-\frac{25}{(5x+2)^2}$$
   • $$-\frac{5}{(5x+2)^2}$$
   • $$-\frac{1}{(5x+2)^2}$$
   • $$-\frac{25}{(5x+2)}$$

10. The region bounded by the parabolas $$y=x^2$$ and $$y=8x-x^2$$ is rotated about the $$x$$-axis so that a vertical line segment cut off by the curves generates a ring. The value of $$x$$ for which the ring of largest area is obtained is:

    • $$1$$
    • $$2$$
    • $$\frac{8}{3}$$
    • $$4$$