# التالي؟ التعبير يكافئ يأتي مما أّي 1 sin x° cos y° cos x° sin y° + ( sin

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• cos x sin y + sin x cos y

(sin( x - y

(sin( x + y

(cos( x + y

(cos ( x - y

. ( 5- , 1 , 0) p

Q

Q (6 , -2 , 7)

Q (-6 , 2 , -7)

Q (6 , 0 , -3)

Q (-6 , 0 , 3)

1

2

• Which of the following is equivalent to the identity below?

cos x sin y + sin x cos y

(sin( x - y

(sin( x + y

(cos( x + y

(cos ( x - y

If the coordinate of the point p are ( 0 , 1 , - 5 ) and .

What are the co-ordinates of Q ?

Q (6 , -2 , 7)

Q (-6 , 2 , -7)

Q (6 , 0 , -3)

Q (-6 , 0 , 3)

1

2

• f(x) =x3 - 2x2 + 3

x +3

x + 1

x 1

x - 3

-2 v

. 2

. 180

. 180 2

.

(f(x f(x) = e

e

- x2 e

e

- e

4

3

5 1 x

-1 x

2

1 x

1 x

1 x 1 .

x 2

• Which of the following is a factor of f(x) =x3 - 2x2 + 3?

x +3

x + 1

x 1

x - 3

Which of the following best describes what happens to a vector v when it

is multiplied by the scalar -2?

The magnitude is multiplied by 2 and the direction is unchanged.

The magnitude is unchanged and the direction is inverted by 180

The magnitude is multiplied by 2 and the direction is changed by 180

The magnitude is unchanged and the direction is unchanged.

If f(x) = e find f(x)?

e

- x2 e

e

- e

3

4

-1 x

2

1 x

1 x 2

1 x

1 x

5 1 x

• .v(t) /

v(t) = 3t2 6t + 7

t = 3 t =0

Centimeters 75

Centimeters 36

21 centimeters

Centimeters 12

f(x) = x2 + 3, 0 x 3

(f(x x

6 square units

9 square units

18 square units

36 square units

6

7

• A particle is traveling along the x-axis with a velocity in centimeters

per second defined by the function v(t).

v(t) = 3t2 6t + 7

What is the displacement of the particle between t = 0 and t = 3

seconds?

centimeters75

centimeters36

21 centimeters

centimeters12

Look at the function.

f(x) = x2 + 3, 0 x 3

What is the area between the function and the x-axis?

6 square units

9 square units

18 square units

36 square units

6

7

• y = cos(2x3 1)

.

x cosx2 dx

u = x 2

2 sinx + c

sin2x + c

2sinx2 + c

sinx2 + c

8

9

• For y = cos(2x3 1 ), find ?

Look at the integral.

x cosx2 dx

Use the substitution u = x2 to evaluate the integral.

2sinx + c sin2x + c

2 sinx2 + c

sinx2 + c

8

9

• [0 ,2]

( g ( - 2 0

( ) ( )x

g x f t dt

- 0.5

0.5

- 1.5

1.5

a b = 0 b a

a b .

a b .

b a

b a

10

11

• The graph of the function f shown figure below is a piecewise continuous

function defined on [2, 0]. The graph of f consists of two line segments.

Let g be the function given by 0

( ) ( )x

g x f t dt . Find g(2) ?

A. - 0.5

B. 0.5

C. - 1.5

D. 1.5

Vectors a and b are non-zero vectors such that a b = 0.

Which statement is true?

Vectors a and b are parallel.

Vectors a and b are perpendicular.

Vector a has the same magnitude as vector b and points in the

same direction.

Vector a has the same magnitude as vector b but points in the

opposite direction.

10

11

• y. y = ln x

[x [0,3 f(x) = 2x - 3 (f(x

f(x (

9

9

36

9

12

13

• Let y = ln x. Find ? for all values in the domain of y.

A function and its domain are shown below.

f(x) = 2x - 3 ; x [0,3]

The function is to be revolved about the x-axis. What will be the

volume formed by that revolution?

9

9

36

36

12

13

• .

3

2

1

3

2

-1

3

-2

1

-3

-2

1

y = 2x + 5:

51

14

• Express the vector in component form.

3

2

1

3

2

-1

3

-2

1

-3

-2

1

.

Find the inverse of the function y = 2x + 5.

15

14

• f(1) = -2 , f ' (1) = 2 , g (1) = 5 , g' (1)= -1 :

g)'(1) ( f :

-12

-2

9

12

dy f (3) = -2 (y = f(3x4 dx

x = 1

12

10

2-

24-

0t v(t) =( 3t2+ 6 t ) ms-1

/ v t

t =1 x = 2

4

6

9

11

16

17

18

• If f(1) = -2 , f ' (1) = 2 , g (1) = 5 and g' (1)= -1 find ( f g)'(1)

-12

-2

9

12

If y = f(3x4), and f(3) = -2, find dydx

at x = 1?

12

10

2

24-

A particle moves along the x-axis with velocity given by 23 6v t t t for time

0t . If the particle is at position x = 2 at time t = 0, what is the position of the

particle at time t = 1?

4

6

9

11

16

18

17

• x = 2 y y = x y = ex

e2 + 1

e2 3

e2 + 3

e2 -1

b b>0

19

20

• Find the area enclosed by the graphs of y = ex, y = x, the y-axis, and the line x = 2 ?

e2 + 1

e2 - 3

e2 + 3

e2 -1

If , b>0 find the value of b?

19

20

• :

. .

21

• Find .

Evaluate the integral. Show your work .

21

• = (f(x 3

13

x

x x 3

( ) (f -1 (x

22

• A function is shown below.

f (x) = 3

13

x

x , x 3.

find the inverse function f -1 (x) for all x , x 3. (show your work)

22

• . y = 2x x2

.x ( ) 360

.A

B .

23

• A part of the graph of y = 2x x2 is given in the diagram below.

A. Write down an expression for this volume of revolution.

B. Calculate this volume.

23

• :

24

• Use partial fractions to integrate.

24

• .

234ln)( xxh

k . 10 x + 3 x4 - 2x2 - k x + 5

25

26

• Find the deriv

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