Question 1

Given the graph of $$f(x) = x + 1 ($$see Image 1), what is $$\lim_{x 	o 1} f(x)$$?

Accepted Answer

$$2$$

Question 2

Which of the following best describes the definition of a limit $$\lim_{x 	o c} f(x) = L$$?

Accepted Answer

As $$x$$ approaches $$c$$, $$f(x)$$ becomes close to $$L$$, but $$x$$ does not have to equal $$c.$$

Question 3

Refer to Image 2. What is $$\lim_{x 	o 3^-} f(x)$$?

Accepted Answer

$$4$$

Question 4

Refer to Image 2. What is $$f(3)$$?

Accepted Answer

$$3$$

Question 5

Refer to Image 3. What is $$\lim_{x 	o 2^+} f(x)$$?

Accepted Answer

$$1$$

Question 6

Refer to Image 3. What is $$f(2)$$?

Accepted Answer

$$-1$$

Question 7

Which of the following must be true for $$\lim_{x 	o c} f(x) to $$exist?

Accepted Answer

The left and right limits exist and are equal.

Question 8

Evaluate $$\lim_{x 	o 2} (x^2$ - 2x + 3). $$Show your steps.

Accepted Answer

$$3$$

Question 9

If $$\lim_{x 	o 4} g(x) = 7$$ and $$\lim_{x 	o 4} h(x) = -5$$, what is $$\lim_{x 	o 4} [h(x) - 2g(x)]$$?

Accepted Answer

$$-19$$

Question 10

Which of the following is an indeterminate form?

Accepted Answer

$$\frac{0}{0}$$

Question 11

Evaluate $$\lim_{x 	o 3} \frac{x^2$ - 9}{x - 3}.$$

Accepted Answer

$$6$$

Question 12

If $$\lim_{x 	o c} f(x) = L$$ and $$\lim_{x 	o c} g(x) = M$$ with $$M 
eq 0$$, what is $$\lim_{x 	o c} \frac{f(x)}{g(x)}$$?

Accepted Answer

$$\frac{L}{M}$$

Question 13

Evaluate $$\lim_{h 	o 0} \frac{f(a+h) - f(a)}{h}$$ for $$f(x) = 7 - 2x.$$

Accepted Answer

$$-2$$

Question 14

Suppose $$f(x) = -2x + 3$$ for $$x  5. $$What is $$\lim_{x 	o 5^-} f(x)$$?

Accepted Answer

$$-7$$

Question 15

Suppose $$f(x) = -2x + 3$$ for $$x  5. $$What is $$\lim_{x 	o 5^+} f(x)$$?

Accepted Answer

$$7$$

Question 16

Suppose $$f(x) = -2x + 3$$ for $$x  5. $$Does $$\lim_{x 	o 5} f(x)$$ exist?

Accepted Answer

No, because the left and right limits are not equal.

Question 17

Evaluate $$\lim_{h 	o 0} \frac{\sqrt{a+h} - \sqrt{a}}{h}$$ for $$a \u003e 0.$$

Accepted Answer

$$\frac{1}{2\sqrt{a}}$$

Question 18

Which property of limits allows you to write $$\lim_{x 	o c} [f(x) + g(x)] = \lim_{x 	o c} f(x) + \lim_{x 	o c} g(x)$$?

Accepted Answer

Sum Law

Business Calculus Study Notes: Introduction to Limits

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