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.

    The shaded region is revolved through 360 about the x-axis.

    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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