Yes, because $$\lim_{x \to 3} f(x) = f(3)$$

No, because $$\lim_{x \to 2} g(x) \neq g(2)$$

$$\lim_{x \to a} \frac{f(x)}{g(x)} = \frac{\lim_{x \to a} f(x)}{\lim_{x \to a} g(x)} if$$ $$\lim_{x \to a} g(x) \neq 0$$

Question 1

Let $$f(x) = 2x + 2. $$What is $$\lim_{x 	o 2.5} f(x)$$?

Accepted Answer

$$7$$

Question 2

Given $$f(x) = x^2$ - 9$$, what is $$\lim_{x 	o 3} f(x)$$?

Accepted Answer

$$0$$

Question 3

Which of the following statements is TRUE about the limit $$\lim_{x 	o a} f(x) = L$$?

Accepted Answer

For all values of $$x$$ sufficiently close to $$a$$, $$f(x) is $$close to $$L.$$

Question 4

Suppose $$f(x) is $$defined as $$f(x) = \frac{x^2$ - 9}{x - 3}. $$What is $$\lim_{x 	o 3} f(x)$$?

Accepted Answer

$$6$$

Question 5

If $$\lim_{x 	o a^-} f(x) = L$$ and $$\lim_{x 	o a^+} f(x) = L$$, what can be concluded?

Accepted Answer

$$\lim_{x 	o a} f(x) = L$$

Question 6

Evaluate $$\lim_{x 	o 0} \sqrt{x^3$ + 12}.$$

Accepted Answer

$$\sqrt{12}$$

Question 7

Find $$\lim_{x 	o \infty} \frac{4x^3$ - 5x^2$ + 4x}{2x^3$ + 9x^2$ + 7}.$$

Accepted Answer

$$2$$

Question 8

Which of the following is NOT a requirement for a function $$f(x) to be $$continuous at $$x=a$$?

Accepted Answer

$$f(x) is $$differentiable at $$x=a$$

Question 9

Given $$h(x) = \begin{cases} x^2$ - 9 & x \u003c 3 \ 7 & x \geq 3 \end{cases}$$, what is $$\lim_{x 	o 3^-} h(x)$$?

Accepted Answer

$$0$$

Question 10

Given $$h(x) = \begin{cases} x^2$ - 9 & x \u003c 3 \ 7 & x \geq 3 \end{cases}$$, what is $$\lim_{x 	o 3^+} h(x)$$?

Accepted Answer

$$7$$

Question 11

Evaluate $$\lim_{x 	o 2} \frac{x^2$ + 5x + 1}{x + 2}.$$

Accepted Answer

$$3.6$$

Question 12

If $$f(x) = x^2$ - 9$$, is $$f(x)$$ continuous at $$x=3$$?

Accepted Answer

Yes, because $$\lim_{x 	o 3} f(x) = f(3)$$

Question 13

Evaluate $$\lim_{x 	o 3} \frac{x^2$ - 7x + 2}{x - 3}.$$

Accepted Answer

$$-5$$

Question 14

Find $$\lim_{x 	o \infty} \frac{2x^2$ + 5x + 1}{4x^2$ + 7}.$$

Accepted Answer

$$\frac{2}{4}$$

Question 15

Suppose $$g(x) = \begin{cases} x - 1 & x \u003c 2 \ 1 & x \geq 2 \end{cases}. Is$$ $$g(x)$$ continuous at $$x=2$$?

Accepted Answer

No, because $$\lim_{x 	o 2} g(x) 
eq g(2)$$

Question 16

Evaluate $$\lim_{x 	o 0} \sqrt{x^3$ + 12}$$ using properties of limits.

Accepted Answer

$$\sqrt{12}$$

Question 17

If $$\lim_{x 	o a} f(x) = 5$$ and $$\lim_{x 	o a} g(x) = 2$$, what is $$\lim_{x 	o a} [f(x) + g(x)]$$?

Accepted Answer

$$7$$

Question 18

Which of the following is the correct property for the limit of a quotient?

Accepted Answer

$$\lim_{x 	o a} \frac{f(x)}{g(x)} = \frac{\lim_{x 	o a} f(x)}{\lim_{x 	o a} g(x)} if$$ $$\lim_{x 	o a} g(x) 
eq 0$$

Limits and Continuity in Business Calculus

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