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⟩

Excuse me professor, but every time I post; the published version looks all wrong compared to the draft.