Solution:

12. If , then t =

Solution:

==>

==>

==>

==>

13. The sum of the solutions of the equation is equal to:

Solution:

==>

or

or

e) The equation of the horizontal asymptote of the graph of f is y = 1

Solution:

Note: All questions are related to the graph of f(x) (When graphing remember the rule )

From the graph we see that part (d) is false.

8. A wheel on a truck has a diameter of 12/p feet. How far will the truck move if the wheel turns through 840 degrees.

a) 26 feet

b) 28 feet

c) 12 feet

d) 18 feet

e) 9 feet

Solution:

9. The domain of the function is:

a) (-¥,-1) U (0, ¥) b) (-1, 1) c) (0, ¥) d) (-¥, 0) U (0, ¥)

e) (-¥ , -1) U (1, ¥)

Solution:

==>

________+_________-1______-_______0______-_______1________+________

Thus, the domain is (-¥ , -1) U (1, ¥)

10. If W(t) is the wrapping function, then W(-17p/3) is equal to:

Solution:

11.

16. Given ln 2 = x and ln 3 = y, then =

Solution:

17. The asymptotes of are given by , where n is an integer, then

Solution:

asymptotes of are the zeros of

==>

==>

Therefore A = 4 and B = 3

18. If b, x, y and z are positive real numbers and , then the expression =

solution:

19.

Solution:

Therefore,

Mathcad check:

__________________THE END________________

Mathcad check:

14. Which of the following is true?

a) for any real number x.

Not true if x < 0

b) If , then x = 1.

c) ln x > 0 for x e (0, 1).

d) log(3+3) = (log 3)(log 3).

e) log x is always a positive real number.

ln x < 0 for x e (0, 1).

The log of sums or differences can not be simplified

The range of log x is (-¥ , ¥)

Solution:

Part (b)

==>

15. The supplementary angle of is:

Solution:

=

----------------------------------------

Mathcad check:

2. If , (a > 0, b > 0) has period p and range [-1, 3], then is equal to:

a)

b)

c)

d)

e)

Solution:

range = [-1, 3] ==>

vertical shift = d =

(Midpoint formula)

Thus,

3. In the adjacent figure, the expression w + 2x =

a)

b)

c)

d)

e)

Solution:

==>

Math 002-043-A. Farhat

Major Exam 1 Solution

July 23, 2005

version 3

1. The solution set of

a) { }

b) { }

c) { }

d) { }

e) { }

Solution:

==>

Cross multiply

==>

Divide by 2 and then multiply both side by

==>

==>

Take log of both sides

==>

Use the property

==>

Mathcad returns the answer in terms of the natural log.

(S > 0 ==> right shift)

Your may also rewrite the function in standard form as and then find the values of A, P and S:

==>

(S > 0 ==> right shift)

6. Suppose that the terminal side of an angle q in standard position lies on the line where , then

a) -3

b) 4

c) -4

d) 3

e) 5

Solution:

Choose a value for x, say x = 1 ==> y = -3

==>

7. If , which one of the following is FALSE?

a) The graph of f is decreasing.

b) The range of f (-¥ , 1) .

c) The graph of f has one x-intercept and on y-intercept

d) The graph of f is above the x-axis for x e (1, ¥)

and

==>

==>

==>

==>

Therefore,

4. If , , then the graph of f is below the x-axis on the interval

a)

b)

c)

d)

e)

Solution:

The graph of is the same as the graph of shifted to the right by p /4 and reflected about the x-axis.

As shown in the graph, the interval where the graph is below the x-axis is (p /4, 5p/4)

5. The function has amplitude A, period P and phase shift S. Then,

a) A = 2, P = 2p /3, S = p /3 to the right

b) A = -2, P = 2p /3, S = p /3 to the left

c) A = 2, P = 2p /3, S = p to the right

d) A = 2, P = p /3, S = p to the right

e) A = -2, P = p /3, S = p to the left

Solution: