Limits & Continuity — Quiz 3

Questions in this quiz (10)

1. $$\lim_{x\to3}\frac{x^3-27}{x^2-9}=?$$

   • $$6$$
   • $$\frac{7}{2}$$
   • $$3$$
   • $$\frac{9}{2}$$

2. $$\lim_{x\to\infty}\frac{7-x^2}{5x^2+2x-4}=?$$

   • $$-\frac{1}{5}$$
   • $$-\frac{2}{5}$$
   • $$\frac{1}{5}$$
   • $$-\frac{1}{3}$$

3. $$\lim_{x\to-\infty}\frac{4x^3-32}{15x^2+6x+1}=?$$

   • $$-5$$
   • The limit diverges to $$-\infty$$
   • $$\infty$$
   • $$0$$

4. $$\lim_{x\to2}\frac{5x^2+40}{x^3-8}=?$$

   • $$-20$$
   • $$\infty$$
   • $$0$$
   • The limit does not exist.

5. $$\lim_{x\to\infty}\frac{3-x}{3^x}=?$$

   • $$0$$
   • $$\frac{1}{3}$$
   • $$\infty$$
   • $$-1$$

6. $$\lim_{x\to\infty}\frac{5-x}{4^x}=?$$

   • $$\frac{1}{4}$$
   • $$\infty$$
   • $$-1$$
   • $$0$$

7. $$\lim_{x\to0}\frac{\sin(7x)}{x}=?$$

   • $$\frac{1}{7}$$
   • $$7$$
   • $$14$$
   • $$1$$

8. $$\lim_{x\to0}\frac{\sin(4x)}{5x}=?$$

   • $$\frac{5}{4}$$
   • $$1$$
   • $$\frac{1}{5}$$
   • $$\frac{4}{5}$$

9. Which of the following statements is correct about the graph of $$y=\arctan(2x)$$?

   • Vertical asymptotes at $$x=0$$ and $$x=\pi$$
   • Horizontal asymptotes at $$y=\pm\frac{\pi}{2}$$
   • Horizontal asymptotes at $$y=0$$ and $$y=\pi$$
   • Vertical asymptotes at $$x=\pm\frac{\pi}{2}$$

10. Which of the following statements is correct about the graph of $$y=\frac{x^2-4}{3x-6}$$?

    • has an infinite discontinuity at $$x=2$$
    • has a vertical asymptote at $$x=2$$
    • has a horizontal asymptote at $$y=\frac{2}{3}$$
    • has a removable discontinuity at $$x=2$$