Calculus Questions

Question Given that a particle travels according to the velocity function v t 2t 7 m sec what is the total distanced traveled by the particle over the time interval 2 5 Enter your answer as an exact fraction if necessary and do not include units in your answer

Find the shortest distance between 10 a and the curve y x 1 Select one a b C d 7 2 11 2 13 2 Lo VR TEA VR TEAM VRT VR

Simplify the following trigonometric expression and verify that it equals sin D 8pts Show all steps cot D tan D sin D cos D Show all work only work typed into the space below will be graded Select the Insert drop down option in the menu below and use Equation to type your answer when you need to incorporate symbols equations or other math expressions

One possible way to simplify the trigonometric expression is shown Choose the correct substitution in each of the steps below from the answer bank provided Simplify secx cos x cotx sinx Step 1 secx cos x A sin x Step 2 secx cos x B Step 3 C cos a Step 4 D Answer Bank M Sin z cas m N Cos where A Select where B Select where C Select where D Select

Find the horizontal asymptote y 2 2 x 2x 3 U y X 2

Find the horizontal asymptote y 3x 6 X E f x

Find the vertical asymptote x L f x 4 2 x 1

Find the horizontal asymptote y Ny 2 1 x 5 x 3x 2

Find the vertical asymptote x A f x x 3 5x 4

Determine whether the following statements are true and give an explanation or counterexample a A pyramid is a solid of revolution b The volume of a hemisphere can be computed using the disk method TR 2 2 Let R be the region bounded by y sin x and the x axis on 0 The volumes of the solids generated when R and R are c Let R be the region bounded by y cos x and the x axis on revolved about the x axis are equal a Choose the correct answer below C OA The statement is false A solid of revolution must have cross sections which are circular i e either disks or washers with the axis of revolution running through the center of the disk A pyramid has circular cross sections so it cannot be a solid of revolution B The statement is false A solid of revolution must have cross sections which are circular i e either disks or washers with the axis of revolution running through the center of the disk A pyramid does not have any circular cross sections so it cannot be a solid of revolution OC The statement is true A solid of revolution must have cross sections which are circular i e either disks or washers with the axis of revolution running through the center of the disk A pyramid has circular cross sections so it cannot be a solid of revolution D The statement s true A solid of revolution must have cross sections which are circular i e either disks or washers with the axis of revolution running through the center of the disk A pyramid does not have any circular cross sections so it cannot be a solid of revolution The cross section of the hemisphere plotted in the xy plane will be a circle with a radius of 2r where r is the radius of the hemisphere The equation of this curve is The area of the disk is then z x b The statement is x y r which can be solved for y y 4 The radius of the disk passing through the point x on the x axis is y x Integrating the differential volume dV 4 x dx from gives the formula

The velocity function below corresponds to the motion of a particle If the velocity is measured in meters per second what is the net displacement of the particle for the first 5 seconds S 6t 2 if 0 t 2 if 2 t 5 4t 2 Enter your answer as an exact fraction if necessary and do not include any units Provide your answer below v t

Question Calculate the area in square units bounded above by f x 7x 2x 20 and below by g x 8x 15x 2 Provide answer holour

Suppose that lim f x 9 and lim g x 3 Compute the limits that exist X 4 X 4 a lim f x 3g x a Select the correct choice below and if necessary fill in the answer box to complete your choice A lim f x 3g x 0 X 4 Type an integer or a simplified fraction OB The limit lim f x 3g x does not exist X 4 b lim f x g x c lim 4f x g x d lim X 4 X 4 X 4 b Select the correct choice below and if necessary fill in the answer box to complete your choice A lim f x g x 27 X 4 Type an integer or a simplified fraction OB The limit lim f x g x does not exist X 4 A c Select the correct choice below and if necessary fill in the answer box to complete your choice OB The limit lim 4f x g x does not exist X 4 OA lim 4f x g x 108 X 4 Type an integer or a simplified fraction OB d Select the correct choice below and if necessary fill in the answer box to complete your choice f x f x g x f x g x lim X 4L Type an integer or a simplified fraction f x f x g x X 41 The limit lim does not exist

Use limits to compute f x f x 1 13x

Determine if the limit below exists If it does exist compute the limit x 3x 18 10 2x lim X 10 Select the correct choice below and if necessary fill in the answer box to complete your choic OA C B 3x 18 lim x 10 10 2x Type an exact answer using radicals as needed The limit does not exist

Suppose that lim f x 9 and lim g x 3 Compute the limits that exist X 4 X 4 a lim f x 3g x X 4 b lim f x g x X 4 c lim 4f x g x X 4 OB The limit lim f x 3g x does not exist X 4 a Select the correct choice below and if necessary fill in the answer box to complete your choice A lim f x 3g x 0 X 4 Type an integer or a simplified fraction OB The limit lim f x g x does not exist X 4 f x x 4f x g x d lim x b Select the correct choice below and if necessary fill in the answer box to complete your choice A lim f x g x 27 X 4 Type an integer or a simplified fraction OA lim 4f x g x X 4 Type an integer or a simplified fraction OB The limit lim 4f x g x does not exist X 4 c S lect the correct choice below and if necessary fill in the answer box to complete your choice

Question Consider the region bounded above by f x 2x 9x 10 and below by g x x 12x 10 Find the area in square units between the two functions Provide your answer below

Suppose that lim f x 9 and lim g x 3 Compute the limits that exist X 4 X 4 a lim f x 3g x X 4 b lim f x g x X 4 A c lim 4f x g x X 4 a Select the correct choice below and if necessary fill in the answer box to complete your choice lim f x 3g x 0 x 4 Type an integer or a simplified fraction B The limit lim f x 3g x does not exist X 4 d lim X 4 f x f x g x OB The limit lim f x g x does not exist X 4 b Select the correct choice below and if necessary fill in the answer box to complete your choice OA lim f x g x X 4 Type an integer or a simplified fraction

5 Determine the y intercept of a line with a slope of 2 that is a tangent to the curve y y x 2 4x 5

A particle travels according to the velocity function shown below where velocity is measured in meters per second Find the net displacement of the particle for the first 5 seconds if 0 t 2 if 2 t 5 Enter your answer as an exact fraction if necessary and do not include any units Provide your answer below 7 O v t 2 3t 4 2

The following limit is a definition of f a Determine the function f x and 6 h 6 66 h lim h 0 The function is f x

Question Given that a particle travels according to the velocity function v t 4t 8 m sec what is the total distanced traveled by the particle over the time interval 0 7 Enter your answer as an exact fraction if necessary and do not include units in your answer Provide your answer below I

Question An amusement park has a marginal cost function C x 1000e 5 where x represents the number of tickets sold an a marginal revenue function given by R x 60 0 1x Assuming that the park has no fixed costs find the total profit generated when selling 550 tickets Round your answer to the nearest dollar

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Question Determine the area in square units of the region bounded by g x 10x 11 and f x x 5x 13 over the inter

Question Determine the area in square units of the region bounded by g x 10x 11 and f x x 5x 13 over the interva 8 3 Provide your answer below

Question Determine the area in square units of the region bounded by g x 7x 7 and f x x 11x 28 over the inter 3 7 incorrect Truagain

Find the limits below lim 2sin x lim x0 et 1 lim 10 1 lim 1 0 5 5 cos x et x 1 t In 1 2t 1 im t

Suppose that a particle moves along a straight line with velocity defined by v t 2t 2 where 0 t 4 in meters per second Find the total distance traveled up to t 4 Provide your answer below

7 The graph shown here is the graph of which of the following equations 3 a y 2x 3 b y x 2 c y x 2 5 4 3 2 5 4 3 2 1 1 3 y TS 5 1 345

2 10 pts Find the slope of the tangent line to y 2 x at x 0 Hint we must use a limit here to get the exact value and then some algebra remember the conjugate

Question Determine the area in square units of the region bounded by g x 7x 7 and f x x 11x 28 over the interval 3 7 Provide your answer below

Use part I of the Fundamental Theorem of Calculus to find the derivative of F x 0 INOTE Enter a function as your answor F x f sin sin t dt

Given At what value of x does the local max of f x occur X t 1 f x 1 cos t dt

Use part I of the Fundamental Theorem of Calculus to find the derivative of 9 y t si t sint dt g y NOTE Enter a function as your answer Make sure that your syntax is correct in romombor to put all the

A hemispherical bowl of radius 6 inches is filled to a depth of h inches where 0 sh 6 Find the volume of water in the bowl as a function of h Check the special cases h 0 and h 6 th 18 h in3 3 The volume of the water in terms of h is Type an exact answer using as needed What is the volume of water when h 0 V 0 Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression

Question 2x What is the value of 8cos x sin x dx Provide your answer below

Calculate the derivative ftant sin x dx 0 dt J1

Find a function f and a positive number a such that f x 12x a 1 2 f t 2 160 dt 62 6x 2 t6

Question What is the value of 7x 6 1 24cos x sin x dx Sorry that s incorrect Try again

Question 1 What is the value of 24cos x sin x dx

0 1 6 e x e x sec e x dx Round your answer to 3 decimal places Evaluate Provide your answer below

Keep your answer in rational form do not approximate Find Dr sin in x dx or bol

Question Find the area in square units bounded above by f x 6x 2x 19 and below by g x 7x 12x 21 Provide your answer below

Evaluate x 0 csc x dx Include the constant C in your answer Provide your answer below

Evaluate I cos cos 3x sin 3x dx Include the constant C in your answer Provide your answer below

Find the volume of the solid formed when the region bounded by the graph of f the x axis and the line x 5 is revolved about the x axis if 0 x 3 if 3 x 4 3x 18 if 4 x 5 X f x 3x 6 CELE 104 5 0

2 Draw a graph of a function that has the following characteristics f 2 0 f x 0 for x 2 f x 0 for 2 x 1 limx 1 1 limx 1 3 f x 0 for all x 1 lim C4

A hemispherical bowl of radius 6 inches is filled to a depth of h inches where 0sh 6 Find the volume of water in the bowl as a function of h Check the special cases h 0 and h 6 The volume of the water in terms of h is in Type an exact answer using as needed

19 Find the distance between the point 6 1 4 and the line x 4 3 y 5 z 1 1 1