数学试题英文版

1.

x2 x 2 0 (a) 2x 5x 6

(b) x32x 222x 4x 5x 25x 6x 5

(c)

1 3 x (d) lnx ln x 1 1

(e) ln 5 2x 3

(f) 2x 5 3

2.

(a) Max, an investment counselor, sets up an investment situation for a client that will return $5000 the first year, $6125 the second year, $7250 the third year, and so on, for 25 years. How much is received from the investment altogether? 462500

(b) Hadleytown has a present population of 100,000, and the population is increasing by 3% each

year.

a. What will the population be in 15 years?

151259

b. How long will it take for the population to double?

24.25 yrs

3.

2x3 3x2 11x 10(a) x2 2x 3

(b)

4x2 2x 10 3x 5 x 1 2

4.

(a) Determine whether f is even, odd, or neither even nor odd

a. f x 2x5 3x2 2

b. f x x3 x7

neither odd

c. f x e x2

even neitherd. f x 1 sinx

(b) Iff x 2x lnx, findf 1 2 andf f 1 .

f 1 2 1 f f 1 4 ln2

(c)

a. f x b. f x

c.

x 2, x 3 f x x2 4(d) Let 1, x 3 11 x f x ln lnx a. Sketch the graph of f

b. Determine whether f is continuous at x = 3.

Yes; f is continuous at x = 3

c. Computelim f x andlim f x

x 2x 2

x 2 limf x x 2 limf x

d. Computelim f x andlim f x x 2x 2

e. Find the vertical and horizontal asymptotes of f if any.

H.A: y 0

V.A: x 2

5. (a)

x

(b)

x

1 (c) limln 2 2 x x

ANS:

6.

(a) A football team consists of 3 players who play in a defense position, 3 players who play in a

midfield position and 5 players who play in a forward position. Three players are chosen to collect a gold medal for the team. Find in how many ways this can be done

a. If the captain, who is a midfield player, must be included, together with one defense and one forward player;

3C1 5C1 15

b. If exactly one forward player must be included, together with any two others

5C1 6C2 75

(b) Find how many different arrangements there are of this nine letters in the words GOLD MEDAL

a.

b. If the two letters D come first and the two letters L come last

5P5 120 ln 2

(i) (ii) (iii) 1711P 494010316800 12

3P6 5! 79833600 C2 7C1 21