Please write everything down in a way I can CTRL- C at least for the last 5 questions - 20 - 25 (writing assessments)

11 of 25 Item 10 Which of the following expressions represents the second derivative of y = In (e] te )? (1 point) Item 11 Item 12 (este = ) Item 13 O d'y ( e te = ) Item 14 d'y ( ex e = ) O ( exte = ) Item 15 O d'y dur2 ! = Item 16 O d'y 4 ( @ # +e- 25 ) Item 17 ( ex te = ) ? Next12 of 25 What is the equation of the line that is normal to the curve y? + In x = 19 at the point (e3, -4)? Item 11 (1 point) Item 12 Oy- 4= - Bey ( I + e ? ) Item 13 O y+ 4 =8e3 (z - e3) Item 14 Oy + 4 = (1 -e3) Item 15 Oy+ 4 = - Bos(1 - e3) Item 16 Oy+4= -8e3 (z - e3) Item 17 Item 18 Next13 of 25 Given the curve defined by the equation In (x - 1) = ax2 - by?, which of the following values represents the value of a if the curve goes through the point (2, 1) and the line tangent to that point has a slope of 1? Item 12 (1 point) Item 13 O a = - Item 14 O a= -7 Item 15 2 Oa= 17 Item 16 O a= 1 Item 17 Oa= = Item 18 Item 19 Next14 of 25 Which of the following values represents the value of the second derivative of y with respect to x for the function defined by In (ry) = I - y at the point (1, 1)? Item 13 (1 point) Item 14 O dy Item 15 O d'y Item 16 2 dy Item 17 : 0 dy Item 18 Item 19 O = Item 20 Next15 of 25 Which of the following values represents (f 1)' (-) where f (x) = (3x - 1)3? Item 14 (1 point) Item 15 O Item 16 O Item 17 Alo ole O Item 18 O Item 19 O Item 20 Item 21 Next16 of 25 Given that yz = 1 , which of the following expressions equals ? Item 15 (1 point) Item 16 O z(I-ylnz) y(y z Iny) Item 17 ay z(z-ylny) y(y z lx) Item 18 z(y :Iny) y(I-y Inz) Item 19 O y(z ylny) z(y zInz) Item 20 y(y z lny) Item 21 r(z-ylnz) Item 25 Next17 of 25 The position of an object moving along a line can be modeled by the function s(t) = kt - 0.81(1 -t2)" where s (t) is the position of the object after t seconds after the object is thrown and k is a constant. What is the object's velocity as a function of time? Item 16 (1 point) Item 17 O v(t) = k - 0.81t(1 - 12)2 Item 18 K O v(t) = t - 0.81t(1 -+2)2 Item 19 21 O v(t) = k + 4.86t(1 -12)2 Item 20 O v(t) = k + 4.86(1 -12)2 Item 21 O v(t) = k - 4. 86t(1 -12)2 Item 22 Next18 of 25 Item 16 You are given a function f (r) and told that the function g (x) = af(), a > 0, has a slope equal to 2 In a at x = 0. Which one of the following functions could be f (I)? (1 point) Item 17 Of (z) =12 Item 18 Of (z) = ex - 1 Item 19 Of (z) = 212 + 4x Item 20 Of (I) = 2cos (1) - 2 Item 21 Of (z) = 2In (z + 1) Item 22 Item 23 Next19 of 25 What is the x-intercept of the line tangent to the graph of y? = x2 + y at the point (-v6, 3) ? Item 17 (1 point) Item 18 O Item 19 O Item 20 O _ 2v6 Item 21 21 O Item 22 O 2v6 Item 23 Item 24 Next20 of 25 Item 18 You are given the functions f () and g (I) = sin (f (I)). Which of the following expressions represents the ratio of the derivatives of these two functions, J'(27 Assume that the domain of g (x) is - 3 of 25 Item 1 Which of the following expressions represents if x and y are related by the equation sin r + siny = 12 + y?? Item 2 (1 point) Item 3 dy 27-COST 2y-cos y Item 4 27 /-cos y Item 5 27-005 y 21-COS I Item 6 O dy 2y-cus y Item 7 Item 8 214-cus y Next4 of 25 Which of the following expressions is the derivative of y = (VI + VI5)"? tem 1 Item 2 (1 point) Item 3 O 4= ;(V23 + Vx5)" (v3x + 5x2) Item 4 0= "(V23+ V25)" * (3 7 + 5V/23) Item 5 0 2 = (13+V25)"-1(V31 + V513) Item 6 4 =n(V13+ V/25)"-1 (v3x + V/5z?) Item 7 OH =n(VI3 + V25)"- 1 (3 /2 + 5V/13) Item Next5 of 25 Which of the following expressions is y' given that y - sin (x - 1)2 (x + 1)]? Item 5 (1 point) Item 6 O y' = - (z-3) (1 -1) cos (z - 1)2 (z + 1)] Item 7 O y' = - (31 -1) (1 - 1) cos (1 - 1)2 (z + 1)] Item 8 21 Item 9 O y' = - (z+3) (x - 1) cos (x - 1)2 (x + 1)] Item 10 o y' = (32 + 1) (x - 1) cos (x - 1)? (z + 1)] Item 11 O y' = (32 - 1) (1 - 1) cos (x - 1)? (x + 1)] Item 12 Next6 of 25 Which of the following expressions represents y' when sin a + cosy = sin (x2) + cos (y?)? Item 6 (1 point) Item 7 Oy = 2z sin (z?)-sin z 2y cos(y?)-cos y Item 8 Oy = 2z sin(12) + sin z Item 9 2y cos(y?) + cus y 21 COS (12) -006 1 Item 10 Oy = 2y sin(y?)-sin y 21 cos (12) +006 I Item 11 Oy = 2y sin(y ) + sin y Item 12 Oy = 2y cos(y?) -cos y 2z sin(z?)-sin z Next7 of 25 Item 6 A curve is defined by the equation cos I = y' - I2. Which of the following values is the best approximation of the slope of the line perpendicular to the graph of the equation at the point (7, -7)? Item 7 (1 point) Item 8 0 -1 Item 9 0 1 Item 10 2 O * Item 11 0 2 Item 12 Item 13 Next8 of 25 Given that In y = I + y, which of the following expressions is equal to- Item 7 (1 point) Item 8 Item 9 O d'y (1-y)? Item 10 O dy (1-y) Item 11 21 d'y (1-y)] Item 12 O 1-2y (1-y)? Item 13 O (1-2y)y (1-y)' Item 14 Next9 of 25 Item 8 Which of the following expressions represents d dy where y = tan -1 (12 + 1)? (1 point) Item 9 Item 10 O Item 11 O Item 12 Item 13 Item 14 O aty Item 15 Next