MATH 1330 Review for Test 2

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

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

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!

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

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

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

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

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

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

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

11. Convert the following into radian measure: 110o

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).

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

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.

15. Evaluate: sin 5𝜋 6 − cos −𝜋 4

16. Evaluate: csc 300° +sec⁡(405°)

17. The coordinate point P 𝑝, 2 3 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.

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

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

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

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.

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