5F13Final - Revision history

Matt Lee at 16:12, 13 April 2015

2015-04-13T16:12:58Z

Grad at 22:28, 20 March 2015

2015-03-20T22:28:53Z

Grad at 22:10, 20 March 2015

2015-03-20T22:10:27Z

Grad at 22:02, 20 March 2015

2015-03-20T22:02:23Z

Grad at 22:01, 20 March 2015

2015-03-20T22:01:33Z

Grad: Created page with "1. Please circle either true or false,
a. (True/False)In a geometric sequence, the common ratio is always positive.
b...."

2015-03-20T21:53:41Z

Created page with "1. Please circle either true or false, a. (True/False)In a geometric sequence, the common ratio is always positive. b...."

New page

1. Please circle either true or false, 
    a. (True/False)In a geometric sequence, the common ratio is always positive. 
    b. (True/False) A linear system of equations always has a solution. 
    c. (True/False) Every function has an inverse. 
    d. (True/False) Trigonometric equations do not always have unique solutions. 
    e. (True/False) The domain of <math>f(x) = \tan^{-1}(x)</math> is all real numbers. 
    f. (True/False) The function <math> \log_a(x)</math> is defined for all real numbers. 

2.Find the domain of the following function. Your answer should be in interval notation <math> f(x) = \frac{1}{\sqrt{x^2-x-2}}</math> 

3. Find f <math>\circ</math> g and its domain if <math>f(x) = x^2+1 \qquad g(x)=\sqrt{x-1}</math>

4. Find the inverse of the following function <math> f(x) = \frac{3x}{2x-1}</math>

5. Solve the following inequality. Your answer should be in interval notation. <math>\frac{3x+5}{x+2}\ge 2</math>

6. Factor the following polynomial completely,     <math>p(x) = x^4 + x^3 + 2x-4 </math>

7. Solve the following equation,      <math> 2\log_5(x) = 3\log_5(4)</math>

8.

@@ Line 1: / Line 1: @@
-. Please circle either true or false,<br>
+<span class = "biglink">[[5_F11_Q1|&nbsp;Question 1&nbsp;]]</span> Please circle either true or false,<br>
 &nbsp;&nbsp;&nbsp;&nbsp;a. (True/False)In a geometric sequence, the common ratio is always positive. <br>
 &nbsp;&nbsp;&nbsp;&nbsp;b. (True/False) A linear system of equations always has a solution. <br>

← Older revision		Revision as of 22:28, 20 March 2015
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	9. Solve the following system of equations <br>		9. Solve the following system of equations <br>
	<center><math> \begin{align} 2x + 3y &= & 1\\ -x + y & = & -3\end{align}</math></center>		<center><math> \begin{align} 2x + 3y &= & 1\\ -x + y & = & -3\end{align}</math></center>
		+
		+	10. Write the partial fraction decomposition of the following, <center> <math> \frac{x+2}{x^3-2x^2+x}</math></center>
		+
		+	11. Solve the following equation in the interval <math> [0, 2\pi)</math> <br>
		+	<center><math> \sin^2(\theta) - \cos^2(\theta)=1+\cos(\theta)</math></center>
		+
		+	12. Given that <math>\sec(\theta) = -2</math> and <math>\tan(\theta) > 0 </math>, find the exact values of the remaining trig functions.
		+
		+	13. Give the exact value of the following if its defined, otherwise, write undefined. <br>
		+	<math>(a) \sin^{-1}(2) \qquad \qquad (b) \sin\left(\frac{-32\pi}{3}\right) \qquad \qquad (c)\sec\left(\frac{-17\pi}{6}\right)</math>
		+
		+	14. Prove the following identity, <br>
		+	<center><math>\frac{1-\sin(\theta)}{\cos(\theta)}=\frac{\cos(\theta)}{1+\sin(\theta)}</math></center>
		+
		+	15. Find an equivalent algebraic expression for the following, <center><math> \cos(\tan^{-1}(x))</math></center>
		+
		+	16. Graph the following, <center><math> -x^2+4y^2-2x-16y+11=0</math></center>
		+
		+	17. Graph the following function, <center><math>f(x) = \log_2(x+1) + 2</math></center> <br>
		+	Make sure to label any asymptotes, and at least two points on the graph.
		+
		+	18. Graph the following function, <center><math>f(x) = \left(\frac{1}{3}\right)^{x+1} + 1</math></center> <br>
		+	Make sure to label any asymptotes, and at least two points on the graph.
		+
		+	19. Consider the following function, <center><math>f(x) = -\sin\left(3x+\frac{\pi}{2}\right)+1</math></center><br>
		+
		+	a. What is the amplitude?<br>
		+	b. What is the period? <br>
		+	c. What is the phase shift? <br>
		+	d. What is the vertical shift? <br>
		+	e. Graph one cycle of f(x). Make sure to label five key points.
		+
		+	20. Consider the following rational function,
		+	<center><math>f(x) = \frac{x^2+x-2}{x^2-1}</math></center> <br>
		+
		+	a. What is the domain of f? <br>
		+	b. What are the x and y-intercepts of f? <br>
		+	c. What are teh vertical and horizontal asymptotes of f, if any? Does f have any holes? <br>
		+	d. Graph f(x). Make sure to include the information you found above.
		+
		+	21. Find the sum <br>
		+	<center><math> 5 + 9 + 13 + \cdots + 49 </math></center>
		+
		+	22. Consider the following sequence, <br>
		+	<center><math> -3, 1, -\frac{1}{3}, \frac{1}{9}, -\frac{1}{27}, \cdots </math></center><br>
		+	a. Determine a formula for <math>a_n</math>, the n-th term of the sequence. <br>
		+	b. Find the sum <math> \displaystyle{\sum_{k=1}^\infty a_k}</math>

← Older revision		Revision as of 22:10, 20 March 2015
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	9. Solve the following system of equations <br>		9. Solve the following system of equations <br>
−	<center><math> \begin{~~matrix~~} 2x &+& 3y &= & 1\\ -x &+& y & = & -3\end{~~matrix~~}</math></center>	+	<center><math> \begin{align} 2x + 3y &= & 1\\ -x + y & = & -3\end{align}</math></center>

← Older revision		Revision as of 22:02, 20 March 2015
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	9. Solve the following system of equations <br>		9. Solve the following system of equations <br>
−	<math> ~~\begin{center}~~ \begin{matrix} 2x &+& 3y &= & 1\\ -x &+& y & = & -3\end{matrix~~}\end{center~~}</math>	+	<center><math> \begin{matrix} 2x &+& 3y &= & 1\\ -x &+& y & = & -3\end{matrix}</math></center>

← Older revision		Revision as of 22:01, 20 March 2015
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	7. Solve the following equation,      <math> 2\log_5(x) = 3\log_5(4)</math>		7. Solve the following equation,      <math> 2\log_5(x) = 3\log_5(4)</math>

−	8.	+	8. Solve the following equation,      <math> 3^{2x} + 3^x -2 = 0 </math>
		+
		+	9. Solve the following system of equations <br>
		+	<math> \begin{center} \begin{matrix} 2x &+& 3y &= & 1\\ -x &+& y & = & -3\end{matrix}\end{center}</math>