I tried uploading a word document, but it didn’t work, so I just will link the Google Doc which has the test.
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Final Review
1) Simplify cos and sin to get real numbers
a) cos(11*pi/12) b) sin(5*pi/12)
2)The vectors v⃗ and v⃗ below are being added. Find the approximate magnitude and directional angle of sum ⃗v = v⃗ + v⃗.
a) ||v⃗||=6, and θ =60◦, and ||v⃗||=2, andθ =180◦
b) ||v⃗||=3.7, and θ =92◦, and ||v⃗||=2.2, and θ =253◦
3) Solve for x without using a calculator.
a) ln(2x + 4) = ln(5x − 5) b) ln(x+6)=ln(x−2)+ln(3)
4) State the domain of the function f and sketch its graph.
a) f(x) = log(x) b)f(x)=log(x+7) c)f(x)=ln(x+5)−1
5) Find the domain, the vertical asymptotes and removable discontinuities of the functions
b)f(x)= x2+2 x2 −6x+8 c) f(x) = 3x+6/x^3 −4x
6)add and subtract the complex numbers
a) (5-2i)+(-2+6i) b) (-9-i)-(5-3i)
7)Divide by long division.
a) x^3−4x^2+2x+1/ x−2. b) x^3+6x^2+7x−2/x+3
8) Find all real roots
a)f(x) = 6x^4 + 25x^3 + 8x^2 − 7x − 2. b) f(x) = 4x^3 + 9x^2 + 26x + 6.
9)Find at least 5 distinct solutions of the equation
a) tan(x) = −1. b) cos(x) = √2/2 c) sin(x) = −√3/2
10) Find the magnitude and directional angle of the vector.
a) ⟨6, 8⟩. b) ⟨−2, 5⟩. c) ⟨−4, −4⟩
6. (5 points) Determine the exact value of sin (pi/12)
1)First break sin(pi/12) into the subtraction of two degrees
sin(pi/12)=sin(pi/3-pi/4)
2)Then we use the angle summation formula
sin(pi/3-pi/4)=sin(pi/3)*cos(pi/3)-cos(pi/3)*sin(pi/4)
3)After find the sin and cos of each angle given
sqrt(3)/2*sqrt(2)/2-1/2*sqrt(2)/2
4) Then simplify the equation
sqrt(6)/2-sqrt(2)/2
5) simplify the equation by combining
sqrt(6)-sqrt(2)/2
Test #3 corrections
We’ll finish up course material on Thursday, but you can get started on remaining Webwork sets now.
- Complex Numbers – Direction
- you can complete all problems now
- “argument” means “angle” or “direction”
- Complex Numbers – Magnitude
- you can complete all problems now
- Complex Numbers – Polar Form
- you can complete most problems now
- you can find the modulus (magnitude) and angle or $a+bi$ form of complex numbers $\zeta$ now
- ignore questions asking you for the product $\zeta_1 \cdot \zeta_2$ or quotient $\zeta_1 \div \zeta_2$ until after Thursday’s class
- Vectors – Components
- you can complete all problems now
- Vectors – Magnitude and Direction
- you can complete all problems now
- Vectors – Unit Vectors
- ignore this set until after Thursday’s class
All Webwork sets have been reopened. You have until Wednesday, December 18 to complete anything you didn’t complete previously. Please note that while most sets are due at 11:59pm, the following sets are due at 11:58pm (these are the sets corresponding to topics we’re discussing now):
- Complex Numbers – Direction
- Complex Numbers – Magnitude
- Complex Numbers – Operations
- Complex Numbers – Polar Form
- Sequences – Binomial Theorem
- Vectors – Components
- Vectors – Magnitude and Direction
- Vectors – Unit Vectors
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