Application of derivatives Questions and Answers

Rewrite 6 sin x 4 cos x as A sin x 4 A e 11 Note should be in the interval T

the given equations are x y 12 and x y 0

10 Below we are given vectors u v and w u 5i 2j k v 4i j k w 2i j k Are these vectors co planar In other words do they lie in the same plane Justify your response

Accurately graph the following quadratic function Make sure to label the 5 points on the graph g x x 3 5 Show Transcribed Text 2 If limx 6 p x 7 and lim x 6 P x 2 find the following limx 6 R x

Solve lim f x X 6 0 lim x 3x 40 X 6 2 1 3 40

Use the Vertical Line Test to determine whether the curve is the graph of a function of x a 3 O is a function b c d is not a function A X is a function is not a function is a function is not a function y A 0

Question 5 0 5 points Listen 6 Use the definition of the derivative to determine f x for f x x I Of x 6 x f x 6 x2 J x x x3 Of x 1 6 x2 6 Of x 1 2

Question 1 0 5 point Listen If g x 4 3x determine the domain of g x 1f O 0 O 0 U 0 3 3

The graph below depicts a function f x Its two asymptotes are indicated The graph below depicts a function g x Its one asymptote is indicated in red 5 4 3 2 3 2 19 2 F 5 lim g f x lim g f x 818 lim g f x 2 1 lim g f x

17 Below we are given vectors u v and W u 5i 2j k v 4i j k w i j Are these vectors co planar In other words do they lie in the same plane Justify your respo

P20 7 2 3x 2 Q The graph of the function f x tanx is given above for the interval a 0 2 ONLY Determine the one sided limit Then indicate the equation of the vertical asymptote Find lim f x 2 This indicates the equation of a vertical asymptote is x Find lim f x This indicator the equation of 2x artic

9 One of the members of your team got called to the counseling office while you were working on this problem in class When they came back they saw that you had graphed the inverse of this function How would you explain your process to your group member In other words given f x explain a method that could be used to draw the graph of f x

5x Guer fx 5x Find the secant line for f x from 1 99 to 2

3 Given f x 5x 3x Find the difference quotient f x h f x h hzo

f x x 25 g x 2x 4 If f x 11 then x

b Obtain the natural representation of the circular helix r u a cos u a sin u bu a 0 b 0 0 leq u infty c Find the arc length of one complete turn of the above helix

Do the following for the function f x 8x 7x a Express the slope of the secant line in terms of x and h b Find msec for h 0 5 0 1 and 0 01 at x 1 What value does msec approach as h approaches c Find the equation for the secant line at x 1 with h 0 01 d Graph f and the secant line found in part c on the same viewing window a Type the slope of the secant line in terms of x and h Simplify your answer Do not factor msec

f x x 2 b Find f x d Graph f x

4 Find the exact value of a cos 5t 6 3 z b 8 when sin 8 2 and 0 6 c cos 8 if tan 8 where 0 it 0 2 1 2

Please write as a decimal 4 75 10000

What is the domain of the function y 2 x 61 O O 0 x O 3 X X 0

Which equation is related to x 10 1 x O x 10 x x 1 O x 10 x 2x 1 x 10 x 1 O Ox 10 x2 1

5 7 To rationalize the denominator of 9 14 you should multiply the expression by which fraction O 5 7 9 14 9 14 9 14 9 14 9 14 14 14

Which expression is equivalent to O O 4 200 2 4 20 2 2 5 5 100 A 10 8

What is the following quotient 1 3 3 4 1 3 4 1 3 4 1 3 EN 2

The speed that a tsunami can travel is modeled by the equation S 356 d where S is the speed in kilometers p hour and d is the average depth of the water in kilometers What is the approximate depth of water for a tsunami traveling at 200 kilometers per hour 0 32 km 0 75 km 1 12 km 3 17 km

nd an equation of the tangent line to the curve at the given po y In x415 2 0

Define the points P 0 0 and Q 5 5 For the vector PQ do the following a Sketch the vector in an xy coordinate system b Compute the magnitude of the vector a Graph the vector PQ Choose the correct graph below OA OB www K OC OD

Given the toolkit function f x 2x find the equation of the transformation g x after a shift to the right 2 and a reflection across the y axis Og x 2x 2 O g x 2 2 Og x 2x 2 Og x 2 x 2

43 Let e be an angle in standard position with point x y on its terminal side Find the following trigonometric function for the given values of x y and r x 3 y 4 r 5 cos A 45 B 3 35 C 5 Siar wich D 5

z ln 2 Express 2 64x y w8 as a product of Three terms z e y 4x 2 8w8

lim h 5 h 6 h h 3h

V 28 Express a 390 angle in terms of radians A 13TT 13T radians 6 B C 11 radians 6 13 radians 12

The average value of f x 6x on the interval 0 x 4 is

1 Use a truth table to show that is a tautology pq p q V q p

Simplify the expression inside the limit if possible Select the correct choice below and if necessary OA lim 5 x 2x 4 x 0 X lim X 0 OB The expression inside the limit cannot be simplified Now evaluate the limit Select the correct choice below and if necessary fill in the answer box to com x5 2x4 4 OA lim X 0 B The limit does not exist and is neither nor o X Type an integer or a simplified fraction

I am always continuous and have a point of inflection at the origin My range is from negative infinity to infinity I am always continuous and have a point of inflection at the origin My range is from negative one to one I am continuous every where except when x is zero which is also where I have a vertical asymptote I have a vertical asymptote at x 0 with a domain of only positive numbers Choose Choose Choose Choose

I am continuous every where except when is zero which is also where I have a vertic asymptote

I am always continuous and have a point inflection at the origin My range is from negative one to one

12 Using the distance formula and the points 2 4 7 6 what is the second step in the solution A d 4 2 6 7 B d 4 2 6 7 C d 7 2 6 4 D d 7 2 6 4

7 Rewrite with absolute value notation 3 x 3 OA x 3 B x 3 OC x s3 O D x 23

6 Rewrite with absolute value notation t 7 or t 7 A t s7 B t 27 C t 7 D t 7

Describe this set by listing the elements B t 3 t 11 and t is an even integer A B 3 5 7 9 11 C 4 6 8 10 D D 3 4 5 6 7 8 9 10 111 4 5 6 7 8 9 10

The graph of a function f x is given in the diagram 1 b 51 4 3 2 1 I 0 5 a What is the average rate of change of f on the interval 0 4 x 1 5 2 d b 3 b Determine a value of a on 0 6 such that the instantaneous rate of change of f approximately equal t the average rate of change found in part a You are only expected to make a visual estimate here but tr be as precise as possible There are multiple possible answers enter only one c a 5 6 7 8 c Order each of the following values from LEAST 1 to GREATEST 4 The average rate of change of f on the interval 4 6 The instantaneous rate of change of fat x 1 1 The average rate of change of f on the interval 0 4 The instantaneous rate of change of f at x 2 7 a LEAST 1 b 2nd c 3rd d GREATEST 4

Let F y z x z xz Evaluate aw F ds for each of the following regions W A x y z 8 B x y2 z 8 x 0 c x y2 z 8 x 0

1 point Evaluate aw F dS where F x y z ex z and W is the solid rectangular box whose sides are bounded by the coordinate planes and th planes x 9 y 3 z 10

1 point Evaluate the line integral 3y dx 4x dy where C is the straight line path from 3 4 to 9 10 c3y dx 4x dy

1 point If F V 2x y find F dr where C is the quarter of the circle x y 16 in the first quadrant oriented counterclockwise JcF dr

Estimate the instantaneous rate of change of g t 2t 2 at the point t 3 In other words choose x values that are getting closer and closer to 3 and compute the slope of the secant lines at each value Then use the trend pattern you see to estimate the slope of the tangent line

Suppose an arrow is shot upward on the moon with a velocity of 59 m s then its height in meters after t seconds is given by h t 59t 0 83t2 Find the average velocity over the given time intervals 3 4 3 3 5 3 3 1 3 3 01 3 3 001