Mini Exam 1 — Timed Mini Exams

Questions in this quiz (10)

1. Which of the following functions is continuous at $$x=0$$?$$A.$$ $$f(x)=\cos\frac{1}{x}$$ for $$x\ne0$$$$f(0)=0$$$$B.$$ $$f(x)=\frac{x^2}{x}$$ for $$x\ne0$$$$f(0)=0$$$$C.$$ $$f(x)=x^2\sin\frac{1}{x}$$ for $$x\ne0$$$$f(0)=0$$$$D.$$ $$f(x)=\frac{x+3}{x}$$

   • $$A$$
   • $$A$$ and $$B$$
   • $$B$$ and $$C$$
   • $$A$$ and $$C$$

2. Which of the following statements about the graph of $$y=\frac{x^2+4}{x^2-4}$$ is not true?

   • The graph is symmetric to the $$y$$-axis.
   • The graph has two vertical asymptotes.
   • The graph has one horizontal asymptote.
   • The graph has an $$x$$-intercept.

3. $$\lim_{x\to1^-}([x]-|x|)=$$?

   • $$-2$$
   • $$-1$$
   • $$0$$
   • $$1$$

4. The $$x$$-coordinate of the point on the curve $$y=x^2-4x+5$$ at which the tangent is perpendicular to the line $$2x+y-4=0$$ is:

   • $$\frac{3}{2}$$
   • $$1$$
   • $$\frac{9}{4}$$
   • $$3$$

5. For a polynomial function $$f$$, suppose $$f''(1)=-3$$, $$f''(3)=0$$, $$f''(5)=4.$$ Which of the following must be true?

   • $$f$$ has an inflection point at $$x=3.$$
   • $$f$$ has a maximum at $$x=3.$$
   • $$f$$ has a root at $$x=3.$$
   • None of the above must be true.

6. $$\int_{0}^{5}|x-3|dx=$$?

   • $$5$$
   • $$\frac{13}{2}$$
   • $$7$$
   • $$\frac{15}{2}$$

7. The maximum value of the function $$f(x)=x^4-3x^3+2$$ on $$[0,3]$$ is:

   • $$2$$
   • $$3$$
   • $$5$$
   • $$8$$

8. If $$\cos x=\ln y$$ and $$0$$ < $$x$$ < $$\pi,$$ then, in terms of $$x,$$ $$\frac{dy}{dx}$$ equals:

   • $$e^{\cos x}\sin x$$
   • $$-e^{\cos x}\sin x$$
   • $$\frac{e^{\cos x}}{\sin x}$$
   • $$e^{\sin x}$$

9. If $$f(x)=x\sin x,$$ then $$f'(\pi)$$ equals:

   • $$\pi$$
   • $$0$$
   • $$-1$$
   • $$-\pi$$

10. An equation of the tangent to the curve $$y=e^x\cos x$$ where $$x=0$$ is:

    • $$y=1$$
    • $$y=1+x$$
    • $$y=1-x$$
    • $$y=e^x$$