Limits & Continuity — Quiz 3
Practice Limits & Continuity — Quiz 3 on The School of Mathematics (Limits & Continuity) with 10 scored questions in about 10 min. This set covers problems such as: “\lim_{x\to3}\frac{x^3-27}{x^2-9}=?”; “\lim_{x\to\infty}\frac{7-x^2}{5x^2+2x-4}=?”; “\lim_{x\to-\infty}\frac{4x^3-32}{15x^2+6x+1}=?”. Work carefully, check explanations for misses, then retake to track improvement before test day.
Questions in this quiz (10)
$$\lim_{x\to3}\frac{x^3-27}{x^2-9}=?$$
- $$6$$
- $$\frac{7}{2}$$
- $$3$$
- $$\frac{9}{2}$$
$$\lim_{x\to\infty}\frac{7-x^2}{5x^2+2x-4}=?$$
- $$-\frac{1}{5}$$
- $$-\frac{2}{5}$$
- $$\frac{1}{5}$$
- $$-\frac{1}{3}$$
$$\lim_{x\to-\infty}\frac{4x^3-32}{15x^2+6x+1}=?$$
- $$-5$$
- The limit diverges to $$-\infty$$
- $$\infty$$
- $$0$$
$$\lim_{x\to2}\frac{5x^2+40}{x^3-8}=?$$
- $$-20$$
- $$\infty$$
- $$0$$
- The limit does not exist.
$$\lim_{x\to\infty}\frac{3-x}{3^x}=?$$
- $$0$$
- $$\frac{1}{3}$$
- $$\infty$$
- $$-1$$
$$\lim_{x\to\infty}\frac{5-x}{4^x}=?$$
- $$\frac{1}{4}$$
- $$\infty$$
- $$-1$$
- $$0$$
$$\lim_{x\to0}\frac{\sin(7x)}{x}=?$$
- $$\frac{1}{7}$$
- $$7$$
- $$14$$
- $$1$$
$$\lim_{x\to0}\frac{\sin(4x)}{5x}=?$$
- $$\frac{5}{4}$$
- $$1$$
- $$\frac{1}{5}$$
- $$\frac{4}{5}$$
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 $$x=\pm\frac{\pi}{2}$$
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 $$x=2$$