1. MATH 1330
Review for Test 2

2. 1. Determine the difference quotient for: f(x) = 2x2 – 5x + 1

3. 2. Determine the difference quotient for: 𝑔 𝑥 = 𝑥+3 𝑥+7

4. 3. Determine the vertical asymptotes, horizontal asymptotes, slant asymptotes, and holes of the function: ℎ 𝑥 = 2 𝑥 2 −4𝑥−30 𝑥 2 −3𝑥−18
Note: Horizontal Asymptotes are also called Limits at Infinity!

5. 4. Determine the vertical asymptotes, horizontal asymptotes, slant asymptotes, and holes of the function: 𝑖 𝑥 = 𝑥 3 −4 𝑥 2 −3𝑥+12 𝑥 2 −3𝑥−4

6. 5. Expand the logarithm: ln 𝑥+5 2 𝑥−3 𝑥 4 𝑥+1

7. 6. Determine all six trigonometric functions of the acute angle θ if csc 𝜃= 5 2

8. 7. In ABC, altitude AD is drawn. <C is 30o and <B is 45o
7. In ABC, altitude AD is drawn. <C is 30o and <B is 45o. If AC = 14. Find the measure of AB. A B C D

9. 8. If f(x) = log2(x + 1) and g(x) = 3x find (gof)(7)

10. 9. If f(x) = log2(x + 1), find f-1(4)

11. 10. Determine the value of: lim 𝑥→∞ 4∙ 2 3 𝑥 +7

12. 11. Convert the following into radian measure: 110o

13. 12. A sector has an area of 9𝜋 5 𝑐𝑚 2 and a radius of 3 cm
12. A sector has an area of 9𝜋 5 𝑐𝑚 2 and a radius of 3 cm. Determine the angle measure (in radians).

14. 13. Determine the angular velocity (in radians per second) of the second hand of a clock.

15. 14. Determine the linear velocity (in inches per second) of the second hand of the same clock, considering the second hand has a length of 9 inches.

16. 15. Evaluate: sin 5𝜋 6 − cos −𝜋 4

17. 16. Evaluate: csc 300° +sec⁡(405°)

18. 17. The coordinate point P 𝑝, lies on the unit circle in the second quadrant. Determine the sinθ and cosθ, where θ represents the angle between the positive x-axis and the segment connecting (0,0) to P.

19. 18. Determine the value of csc θ given that cos θ = 3/5 and sin θ < 0.

20. 19. Simplify the trigonometric expression: sin 𝜇 1+ cos 𝜇 + 1+ cos 𝜇 sin 𝜇

22. 20. Simplify the Trigonometric Expression: 1− cot 2 (𝛼) 1+ cot 2 (𝛼) +2 cos 2 (𝛼)

24. Circle C has the equation x2 + y2 = k for a constant k
Circle C has the equation x2 + y2 = k for a constant k. Line m passes through the point (0,0) and intersects the circle at (-2,7). Determine sec(theta) where theta is the angle between the positive x-axis and line m.

26. Popper 5: Fill out answer choice A for #1 – 5.