## Description

1.

Using the graph of f(x) below, find

(4 points)

2.

Find . (4 points)

3.

What is ? (4 points)

4.

What is ? (4 points)

5.

Find the limit of the function by using direct substitution

(4 points)

1.

If and , then . (4 points)

2.

Find the limit of the function algebraically.

(4 points)

3.

Find . (4 points)

4.

Evaluate . (4 points)

5.

Evaluate . (4 points)

1.

Evaluate (6 points)

2.

Find the equation of the horizontal asymptote for the function, . (7 points)

3.

Which of the following is false for ? (7 points)

1.

To two decimal places, find the value of *k* that will make the function f(x) continuous everywhere.

(4 points)

2.

Where is discontinuous? (4 points)

3.

Is the function continuous? (4 points)

4.

List the discontinuities for the function f(x) = cot( ). (4 points)

5.

Which of the following is true for ? (4 points)

What is the instantaneous slope of y = at x = -3? ( 4 points)

2.

What is the average rate of change of y with respect to x over the interval [-2, 6] for the function y = 5x + 2? (4 points)

3.

What is the slope for the function y = -5x^{2} + 2 at the point x = 1? (4 points)

4.

The surface area, S, of a sphere of radius r feet is S = S(r) = 4πr^{2}. Find the instantaneous rate of change of the surface area with respect to the radius r at r = 4. (4 points)

5.

A ball is thrown vertically upward from the top of a 100 foot tower, with an initial velocity of 10 ft/sec. Its position function is s(t) = -16t^{2} + 10t + 100. What is its velocity in ft/sec when t = 2 seconds? (4 points)

## Explanation & Answer

All answers was tested, so please use them. Ask if something is unclear.docx and pdf files are identical

1. B, does not exist. (we can say it is −∞ but no such option).

3

2. D, − 2 (because sin(−3𝑥 ) ~ − 3𝑥, sin(2𝑥 ) ~2𝑥).

3. D, −∞ (𝑥 → −4, 𝑥 + 4 → 0+ ).

25 −𝑥

4. B, -10 (√𝑥 −5 =

(5−√𝑥 )(5+√𝑥)

√𝑥−5

= −(5 + √ 𝑥)).

5. D, -5 (obvious).

1. A, TRUE (that limit is 3 ∙ 22 − 4 ∙ 4 = 12 − 16 = −4).

2. C, 10 (the function is equal to 𝑥 + 5).

3. A, 2 (the same from both sides).

4. C, 0 (1 − cos 2 𝑥 = sin2 𝑥 ,

sin2 𝑥

𝑥

= sin 𝑥 ∙

sin 𝑥

𝑥

→ 0).

5. C, 1 (direct substitution).

1. B, −∞ (the denominat...

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