Mathematics for Management -- Supplementary Electronic Materials

Quiz: Limits

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1. What is the value of $\lim_{x \to 0} (x^2 - 5)$ (if it exists)?

does not exist $ 0 $ $ 5 $ $ -5 $

2. Determine the value of the following limit (if it exists) $$ \lim_{x \to -4} \frac{x}{x+4} \, . $$

$ 0 $ $ -4 $ $ 11 $ does not exist

3. Determine the value of the following limit (if it exists) $$ \lim_{x \to 0} \frac{x^8-1}{x-1} \, . $$

$ -1 $ $ 0 $ $ 1 $ does not exist

4. Let $f(x) = x^2 + 5x + 1$. Determine the value of the limit $\lim_{x \to 2} f(x)$ (if it exists).

$ 15 $ $ 1 $ $ 9 $ $ 6 $

5. If $\lim_{x \to a} f(x) = 2$ and $\lim_{x \to a} g(x) = 4$, then $\lim_{x \to a} \left( 3 (f(x))^2 - 4 g(x) \right)$ is (if it exists)

$ -4 $ $ 4 $ $ -10 $ does not exist

6. Determine the value of the following limit (if it exists) $$ \lim_{x \to 2} \frac{x^2 - 4}{x^2 + 4} \, . $$

$ 1 $ $ 0 $ $ -\frac{1}{2} $ $ -1 $

7. Determine the value of the following limit (if it exists) $$ \lim_{x \to -3} \frac{x^2 + 6x + 9}{x^2 + 2x - 3} \, . $$

$ -1 $ $ \frac{3}{2} $ $ 0 $ does not exist

8. Determine the value of the following limit (if it exists) $$ \lim_{x \to 2} \frac{x^3 - 8}{x^2 - 4} \, . $$

$ 0 $ $ 4 $ $ 3 $ does not exist

9. Determine the value of the following limit (if it exists) $$ \lim_{x \to 0} \left( \frac{2x^2 - 3x + 4}{x} + \frac{5x-4}{x} \right) \, . $$

$ 5 $ $ 4 $ $ 3 $ $ 2 $

10. Suppose the total cost, $C(q)$, of producing a quantity $q$ of a product equals a fixed cost of $1000$ GEL plus $3$ GEL times the quantity produced. So total cost in GEL is $C(q) = 1000 + 3q$. The average cost per unit quantity, $A(q)$, equals the total cost, $C(q)$, divided by the quantity produced, $q$. Find the limiting value of the average cost per unit as $q$ tends to $0$ from the right. In other words find $\lim_{q \to 0} A(q)$ (if it exist).

$ 0 $ $ 3 $ $ 1000 $ does not exist

Your grade is: __ of 10

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Solution: 1c; 2d; 3c; 4a; 5a; 6b; 7c; 8c; 9d; 10d

Here, a, b, c, d indicate the 1st, 2nd, 3rd, and 4th answer choice, respectively, for the numbered questions.