Infinite Limits

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Show your work for each problem.

1.
Find $\lim_{x \to 0} \frac{1}{x^2}$ .
1. a) $-\infty$
2. b) $0$
3. c) $1$
4. d) $\infty$
2.
The function $f(x) = \frac{7}{x-6}$ has a vertical asymptote $x = a$ . What is $a$ ?
3.
Find $\lim_{x \to 5^+} \frac{1}{x-5}$ .
4.
Where is the vertical asymptote of $f(x) = \frac{3}{x+5}$ ?
1. a) $x = 5$
2. b) $y = 0$
3. c) $x = 3$
4. d) $x = -5$
5.
For $f(x) = \frac{1}{(x-2)^2}$ , compute $f(2.01)$ .
6.
Find $\lim_{x \to 0} \frac{3}{x^2}$ .
7.
Find the vertical asymptote of $g(x) = \frac{x+4}{x-1}$ .
8.
Find $\lim_{x \to 4^-} \frac{2}{x-4}$ .
1. a) $-\infty$
2. b) $0$
3. c) $\infty$
4. d) $2$
9.
For $f(x) = \frac{1}{x-2}$ , compute $f(1.999)$ .
10.
Find $\lim_{x \to 1^-} \frac{x+3}{x-1}$ .
11.
What is true about $\lim_{x \to 1} \frac{1}{x-1}$ ?
1. a) $\infty$
2. b) $-\infty$
3. c)It does not exist
4. d) $1$
12.
Find the one-sided limits and the two-sided limit of $f(x) = \frac{x}{x-1}$ at $x = 1$ .
13.
How many vertical asymptotes does $f(x) = \frac{x+1}{x^2-4x+3}$ have?
14.
Find $\lim_{x \to -2} \frac{x-3}{(x+2)^2}$ .
15.
Which function has a vertical asymptote at $x = 3$ ?
1. a) $\frac{1}{x+3}$
2. b) $\frac{x-3}{x^2-9}$
3. c) $\frac{x+3}{x-3}$
4. d) $\frac{x^2-9}{x-3}$
16.
The function $f(x) = \frac{x^2-1}{x^2+2x-3}$ has exactly one vertical asymptote $x = a$ . What is $a$ ?
17.
Analyze $f(x) = \frac{x^2-4}{x^2-5x+6}$ at the zeros of its denominator.
18.
Find $\lim_{x \to 2^+} \frac{x^2+1}{4-x^2}$ .