Exponential and Logarithmic Functions Exam



MATH 31, TRIG & LOGS Name _______________

Date _______________

1. Evaluate using limit rules:

a)

b)

[4]

2. Differentiate with respect to x; solve for [pic]. Be sure to simplify your answers; use the best trig ratios possible.

a)

b)

c)

[6]

3. Find the local maximum and/or minimum values for:

Justify by using regions of increase and decrease OR the second derivative test.

[3]

4. SOLVE ONLY ONE of the TWO TRIG PROBLEMS:

• A lighthouse is located on a rocky but straight section of shoreline. The lighthouse lens rotates at a rate of . A boat travelling near the lighthouse maintains a constant distance of 600 m from the shoreline. The distance from the lighthouse to point R on this section of shoreline is 800 m. How fast does the lighthouse beacon beam sweep across the bow of the ship when the ship is directly across from point R? Rounded to nearest m/s.

[4]

4. SOLVE ONLY ONE of the TWO TRIG PROBLEMS:

• A 5.0 metre long ladder rests against a vertical wall. A force is applied to the base of the ladder causing it to slide away from the wall at a speed of 2.0 m/s. How fast is the angle between the top of the ladder and the wall changing when that angle is [pic]

[4]

5. Differentiate with respect to x. Answer in simplest form.

a)

b)

c)

d)

[8]

6. Differentiate with respect to x. Answer in simplest form.

a)

b)

[5]

7. Discuss the curve under the following headings. Answer with exact values in simplest form.

a) Intercepts.

b) Asymptotes.

c) Intervals of increase or decrease.

[4]

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