$$x \geq 1, x \neq 2, x \neq -2$$

Question 1

Which of the following is the domain of the function $$f(x) = \frac{x^2$-9}{x^2$-4}$$?

Accepted Answer

$$x 
eq 2, x 
eq -2$$

Question 2

Find the domain of the function $$f(x) = \sqrt{x-3}.$$

Accepted Answer

$$x \geq 3$$

Question 3

Which value of $$x$$ makes the function $$f(x) = \frac{2x-5}{x^2$-9}$$ undefined?

Accepted Answer

$$x = 3$$ and $$x = -3$$

Question 4

Find the domain of $$f(x) = \sqrt{2x-8}.$$

Accepted Answer

$$x \geq 4$$

Question 5

Given $$f(x) = 2x^2$ - 3x + 7$$ and $$g(x) = 2x - 5$$, find $$(f \circ g)(x).$$

Accepted Answer

$$2(2x-5)^2 - 3(2x-5) + 7$

Question 6

Evaluate $$\lim\limits_{x 	o 2} \frac{x^2$-4}{x-2}.$$

Accepted Answer

$$4$$

Question 7

Find $$\lim\limits_{x 	o 1} \frac{\sqrt{x+3}-2}{x-1}.$$

Accepted Answer

$$\frac{1}{4}$$

Question 8

A chemical reaction rate is modeled by $$R(t) = \frac{5t}{t^2$+1}. $$What is $$\lim\limits_{t 	o 0} R(t)$$?

Accepted Answer

$$0$$

Question 9

Evaluate $$\lim\limits_{x 	o 0} \frac{\sin(3x)}{2x}.$$

Accepted Answer

$$\frac{3}{2}$$

Question 10

Find the domain of $$f(x) = \frac{\sqrt{x-1}}{x^2$-4}.$$

Accepted Answer

$$x \geq 1, x 
eq 2, x 
eq -2$$

Question 11

Evaluate $$\lim\limits_{x 	o 0} \frac{e$$^{2x}$$-1}{x}.$$

Accepted Answer

$$2$$

Question 12

A medication's concentration in the bloodstream is modeled by $$C(t) = \frac{10}{t^2$+1}. $$What is $$\lim\limits_{t 	o \infty} C(t)$$?

Accepted Answer

$$0$$

Question 13

Find $$\lim\limits_{x 	o 1} \frac{x^2$-1}{x-1}.$$

Accepted Answer

$$2$$

Question 14

Evaluate $$\lim\limits_{x 	o 0} \frac{	an(3x)}{2x}.$$

Accepted Answer

$$\frac{3}{2}$$

Question 15

Find the domain of $$f(x) = \frac{1}{\sqrt{x-2}}.$$

Accepted Answer

$$x \u003e 2$$

Question 16

Given $$f(x) = x^2$ - 3x + 7$$ and $$g(x) = 2x - 5$$, find $$(g \circ f)(x).$$

Accepted Answer

$$2(x^2 - 3x + 7) - 5$

Question 17

Evaluate $$\lim\limits_{x 	o 0} \frac{\sin(5x)}{x}.$$

Accepted Answer

$$5$$

Question 18

A population model is given by $$P(t) = \frac{1000}{t^2$+1}. $$What is $$\lim\limits_{t 	o \infty} P(t)$$?

Accepted Answer

$$0$$

Question 19

Find the domain of $$f(x) = \sqrt{5-x}.$$

Accepted Answer

$$x \leq 5$$

Question 20

Evaluate $$\lim\limits_{x 	o 0} \frac{\sin(2x)}{x}.$$

Accepted Answer

$$2$$

Domains and Limits in Calculus: Rational, Radical, and Composite Functions

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