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

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<ul><li><p> cos x sin y + sin x cos y </p><p> (sin( x - y </p><p> (sin( x + y </p><p> (cos( x + y </p><p> (cos ( x - y </p><p> . ( 5- , 1 , 0) p </p><p>Q </p><p> Q (6 , -2 , 7) </p><p>Q (-6 , 2 , -7) </p><p>Q (6 , 0 , -3) </p><p> Q (-6 , 0 , 3) </p><p>1 </p><p>2 </p></li><li><p>Which of the following is equivalent to the identity below? </p><p>cos x sin y + sin x cos y </p><p>(sin( x - y </p><p>(sin( x + y </p><p>(cos( x + y </p><p>(cos ( x - y </p><p>If the coordinate of the point p are ( 0 , 1 , - 5 ) and . </p><p>What are the co-ordinates of Q ? </p><p>Q (6 , -2 , 7) </p><p>Q (-6 , 2 , -7) </p><p>Q (6 , 0 , -3) </p><p>Q (-6 , 0 , 3) </p><p>1 </p><p>2 </p></li><li><p> f(x) =x3 - 2x2 + 3 </p><p> x +3 </p><p> x + 1 </p><p> x 1 </p><p> x - 3 </p><p> -2 v </p><p>. 2 </p><p>. 180 </p><p>. 180 2 </p><p>. </p><p> (f(x f(x) = e </p><p> e </p><p>- x2 e </p><p>e </p><p>- e </p><p>4 </p><p>3 </p><p>5 1 x </p><p>-1 x</p><p> 2 </p><p>1 x </p><p>1 x </p><p>1 x 1 . </p><p>x 2 </p></li><li><p>Which of the following is a factor of f(x) =x3 - 2x2 + 3? </p><p> x +3 </p><p> x + 1 </p><p> x 1 </p><p> x - 3 </p><p>Which of the following best describes what happens to a vector v when it </p><p>is multiplied by the scalar -2? </p><p>The magnitude is multiplied by 2 and the direction is unchanged. </p><p>The magnitude is unchanged and the direction is inverted by 180 </p><p>The magnitude is multiplied by 2 and the direction is changed by 180 </p><p>The magnitude is unchanged and the direction is unchanged. </p><p>If f(x) = e find f(x)? </p><p> e </p><p>- x2 e </p><p>e </p><p>- e </p><p>3 </p><p>4 </p><p>-1 x</p><p> 2 </p><p>1 x </p><p> 1 x 2 </p><p>1 x </p><p>1 x </p><p>5 1 x </p></li><li><p> .v(t) / </p><p>v(t) = 3t2 6t + 7 </p><p> t = 3 t =0 </p><p> Centimeters 75 </p><p> Centimeters 36 </p><p>21 centimeters </p><p> Centimeters 12 </p><p>f(x) = x2 + 3, 0 x 3 </p><p> (f(x x </p><p>6 square units </p><p> 9 square units </p><p> 18 square units </p><p> 36 square units </p><p>6 </p><p>7 </p></li><li><p>A particle is traveling along the x-axis with a velocity in centimeters </p><p>per second defined by the function v(t). </p><p>v(t) = 3t2 6t + 7 </p><p>What is the displacement of the particle between t = 0 and t = 3 </p><p>seconds? </p><p> centimeters75 </p><p> centimeters36 </p><p>21 centimeters </p><p> centimeters12 </p><p>Look at the function. </p><p>f(x) = x2 + 3, 0 x 3 </p><p>What is the area between the function and the x-axis? </p><p> 6 square units </p><p> 9 square units </p><p> 18 square units </p><p> 36 square units </p><p>6 </p><p>7 </p></li><li><p> y = cos(2x3 1) </p><p>. </p><p>x cosx2 dx </p><p> u = x 2 </p><p>2 sinx + c </p><p>sin2x + c </p><p> 2sinx2 + c </p><p>sinx2 + c </p><p>8 </p><p>9 </p></li><li><p> For y = cos(2x3 1 ), find ? </p><p>Look at the integral. </p><p>x cosx2 dx </p><p>Use the substitution u = x2 to evaluate the integral. </p><p>2sinx + c sin2x + c </p><p> 2 sinx2 + c </p><p> sinx2 + c </p><p>8 </p><p>9 </p></li><li><p> [0 ,2] </p><p>( g ( - 2 0</p><p>( ) ( )x</p><p>g x f t dt </p><p> - 0.5 </p><p> 0.5 </p><p> - 1.5 </p><p> 1.5 </p><p>a b = 0 b a </p><p> a b .</p><p> a b .</p><p> b a </p><p> b a </p><p>10 </p><p>11 </p></li><li><p>The graph of the function f shown figure below is a piecewise continuous </p><p>function defined on [2, 0]. The graph of f consists of two line segments. </p><p>Let g be the function given by 0</p><p>( ) ( )x</p><p>g x f t dt . Find g(2) ? </p><p> A. - 0.5 </p><p> B. 0.5 </p><p> C. - 1.5 </p><p> D. 1.5 </p><p>Vectors a and b are non-zero vectors such that a b = 0. </p><p>Which statement is true? </p><p> Vectors a and b are parallel. </p><p>Vectors a and b are perpendicular. </p><p>Vector a has the same magnitude as vector b and points in the </p><p> same direction. </p><p>Vector a has the same magnitude as vector b but points in the </p><p> opposite direction. </p><p>10 </p><p>11 </p></li><li><p> y. y = ln x </p><p> [x [0,3 f(x) = 2x - 3 (f(x </p><p> f(x ( </p><p> 9 </p><p> 9 </p><p> 36 </p><p> 9 </p><p>12 </p><p>13 </p></li><li><p>Let y = ln x. Find ? for all values in the domain of y. </p><p>A function and its domain are shown below. </p><p>f(x) = 2x - 3 ; x [0,3] </p><p>The function is to be revolved about the x-axis. What will be the </p><p>volume formed by that revolution? </p><p> 9 </p><p> 9 </p><p> 36 </p><p> 36 </p><p>12 </p><p>13 </p></li><li><p>. </p><p>3</p><p> 2</p><p>1</p><p> 3</p><p> 2</p><p>-1</p><p> 3</p><p>-2</p><p> 1</p><p> -3</p><p>-2</p><p> 1</p><p> y = 2x + 5: </p><p>51 </p><p>14 </p></li><li><p>Express the vector in component form. </p><p>3</p><p> 2</p><p>1</p><p> 3</p><p> 2</p><p>-1</p><p> 3</p><p>-2</p><p> 1</p><p> -3</p><p>-2</p><p> 1</p><p>. </p><p> Find the inverse of the function y = 2x + 5. </p><p>15 </p><p>14 </p></li><li><p> f(1) = -2 , f ' (1) = 2 , g (1) = 5 , g' (1)= -1 : </p><p> g)'(1) ( f : </p><p> -12 </p><p> -2 </p><p> 9 </p><p> 12 </p><p>dy f (3) = -2 (y = f(3x4 dx</p><p> x = 1 </p><p> 12 </p><p> 10 </p><p> 2- </p><p> 24- </p><p>0t v(t) =( 3t2+ 6 t ) ms-1 </p><p> / v t </p><p> t =1 x = 2 </p><p>4 </p><p> 6 </p><p>9 </p><p> 11 </p><p>16 </p><p>17 </p><p>18 </p></li><li><p>If f(1) = -2 , f ' (1) = 2 , g (1) = 5 and g' (1)= -1 find ( f g)'(1) </p><p>-12 </p><p>-2 </p><p>9 </p><p>12 </p><p>If y = f(3x4), and f(3) = -2, find dydx</p><p> at x = 1? </p><p> 12 </p><p>10 </p><p>2 </p><p>24- </p><p>A particle moves along the x-axis with velocity given by 23 6v t t t for time </p><p>0t . If the particle is at position x = 2 at time t = 0, what is the position of the </p><p>particle at time t = 1? </p><p> 4 </p><p> 6 </p><p> 9 </p><p>11 </p><p>16 </p><p>18 </p><p>17 </p></li><li><p> x = 2 y y = x y = ex </p><p>e2 + 1 </p><p> e2 3 </p><p> e2 + 3 </p><p>e2 -1 </p><p> b b&gt;0 </p><p>19 </p><p>20 </p></li><li><p>Find the area enclosed by the graphs of y = ex, y = x, the y-axis, and the line x = 2 ? </p><p> e2 + 1 </p><p> e2 - 3 </p><p> e2 + 3 </p><p> e2 -1 </p><p>If , b&gt;0 find the value of b? </p><p>19 </p><p>20 </p></li><li><p> : </p><p> . . </p><p>21 </p></li><li><p> Find . </p><p>Evaluate the integral. Show your work . </p><p>21 </p></li><li><p> = (f(x 3</p><p>13</p><p>x</p><p>x x 3 </p><p> ( ) (f -1 (x </p><p>22 </p></li><li><p>A function is shown below. </p><p>f (x) = 3</p><p>13</p><p>x</p><p>x , x 3. </p><p>find the inverse function f -1 (x) for all x , x 3. (show your work) </p><p>22 </p></li><li><p> . y = 2x x2 </p><p> .x ( ) 360 </p><p>.A </p><p>B . </p><p>23 </p></li><li><p>A part of the graph of y = 2x x2 is given in the diagram below. </p><p>The shaded region is revolved through 360 about the x-axis. </p><p> A. Write down an expression for this volume of revolution. </p><p> B. Calculate this volume. </p><p>23 </p></li><li><p>: </p><p>24 </p></li><li><p>Use partial fractions to integrate. </p><p>24 </p></li><li><p>. </p><p>234ln)( xxh </p><p> k . 10 x + 3 x4 - 2x2 - k x + 5 </p><p>25 </p><p>26 </p></li><li><p>Find the derivative of function 234ln)( xxh </p><p> When x4 - 2x2 k x + 5 is divided by x + 3, the remainder is 10. Find k. </p><p>25 </p><p>26 </p></li><li><p>. </p><p> a = 3i + j 2k b = 2i 5j k </p><p> 2: 2log 5 + 2log . 3</p><p> . </p><p>27 </p><p>28 </p></li><li><p>Find the angle between the two vectors a = 3i + j 2k and b = 2i 5j k. </p><p>Express as a single logarithm 2 2log 5 + 2log 3 . </p><p>27 </p><p>28 </p></li><li><p> f(x) = x3 3x2 + 5 </p><p>29 </p></li><li><p> using the second derivative test , </p><p>Find the local maximum and local minimum for </p><p> f(x) = x3 3x2 + 5 </p><p>29 </p></li></ul>

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