Mini Exam 3 — Timed Mini Exams

Questions in this quiz (10)

1. $$\lim_{x\to\infty}\frac{2x^2-5x+1}{6x^2+7}=$$?

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

2. $$\int_{0}^{1}e^x\,dx$$ equals:

   • $$1-e$$
   • $$e-1$$
   • $$\frac{1}{e}-1$$
   • $$e+1$$

3. The volume obtained by rotating the region bounded by $$x=y^2$$ and $$x=3-y^2$$ about the $$y$$-axis is equal to:

   • $$\frac{8\pi}{3}$$
   • $$\frac{16\pi}{3}$$
   • $$\frac{32\pi}{3}$$
   • $$12\pi\sqrt{\frac{3}{2}}$$

4. The general solution of the differential equation$$\frac{dy}{dx}=\frac{2x}{y}$$ is a family of:

   • circles
   • hyperbolas
   • parabolas
   • ellipses

5. Estimate $$\int_{0}^{6}\sqrt{36-x^2}\,dx$$ using a left rectangular sum with two subintervals of equal width.

   • $$9+3\sqrt{27}$$
   • $$9+3\sqrt{18}$$
   • $$12+3\sqrt{18}$$
   • $$18+3\sqrt{27}$$

6. The number of values of $$k$$ for which $$f(x)=e^x$$ and $$g(x)=k\cos x$$ have a common point of tangency is:

   • $$0$$
   • $$1$$
   • large but finite
   • infinite

7. The curve $$x^2y+y^2=3x+2$$ passes through $$(2,1)$$. Use the line tangent to the curve there to find the approximate value of $$y$$ at $$x=2.1$$.

   • $$0.98$$
   • $$1.10$$
   • $$1.15$$
   • $$1.20$$

8. $$\lim_{h\to0}\frac{e^h-1}{h}$$ equals:

   • $$0$$
   • $$1$$
   • $$e$$
   • $$\ln e$$

9. The slope field shown here is for the differential equation:

   • $$y'=\frac{1}{x}$$
   • $$y'=\ln x$$
   • $$y'=e^x$$
   • $$y'=y^2$$

10. What is the domain of the particular solution, $$y=f(x),$$ for $$\frac{dy}{dx}=\frac{4x}{x^2-9}$$ containing the point $$(1,\ln4)$$?

    • $$x$$ < $$-3$$
    • $$x$$ > $$3$$
    • $$-3$$ < $$x$$ < $$3$$
    • $$x\ne\pm3$$