Calculus Questions

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Find the rational number representation of the repeating decimal 0 945

Determine whether the sequence associated with the series is arithmetic or geometric n 2 2 n 0 arithmetic O geometric Find the common difference or ratio Find the sum of the first 15 terms

Find the sequence of the first five partial sums S S S3 S4 and Ss of the geometric sequence by adding terms 8 12 18 27 81 2 S S S3 S4 S5

Find the rational number representation of the repeating decimal 0 945

Find a formula for the nth term of the geometric sequence Then find the indicated nth term of the geometric sequence 7th term 2 14 98 an

Write the first five terms of the geometric sequence Find the common ratior and write the nth term of the sequence as a function of n 16 1 31 a a3 34 a5 r S 11

A 60 m long chain hangs vertically from a cylinder attached to a winch Assume there is no friction in the system and that the chain has a density of 6 kg m Use 9 8 m s for the acceleration due to gravity a How much work is required to wind the entire chain onto the cylinder using the winch b How much work is required to wind the chain onto the cylinder if a 40 kg block is attached to the end of the chain E a Set up the integral that gives the work required to wind the entire chain onto the cylinder using the winch Use increasing limits of integration SO dy Type exact answers

Determine whether or not the sequence is geometric If it is find the common ratio r If an answer does not exist enter DNE 11 26 41 56 O Yes the sequence is geometric O No the sequence is not geometric

Suppose 15000 is invested at 8 interest compounded continuously How long will it take for the investment to grow to 30000 Use the model A t Pert and round your answer to the nearest hundredth of a year years for the investment to reach 30000 It will take

Find the mass of the thin bar with the given density function p x x x 14 x 2 for 0 x 3 The mass of the thin bar is Type an exact answer units

The gravity on the moon is known to be constant at approximately 1 62 m s Suppose while on the moon a rock is thrown such that after 1 second its velocity is 12 m s and its height is 17 m above the moon s surface Using concepts and notation from calculus a Determine the position function of the rock s t b Determine the maximum height of the rock

How much work is required to move an object from x 1 to x 6 measured in meters in the presence of a force in N given by F x Set up the integral that gives the work done dx Type exact answers www 3 acting along the x axis

A spring on a horizontal surface can be stretched and held 0 5 m from its equilibrium position with a force of 65 N a How much work is done in stretching the spring 2 5 m from its equilibrium position b How much work is done in compressing the spring 3 5 m from its equilibrium position a Set up the integral that gives the work done in stretching the spring 2 5 m from its equilibrium position Use increasing limits of integration dx www Type exact answers

Use a change of variables or the table to evaluate the following indefinite integral 8 Sx x 1 d dx Click the icon to view the table of general integration formulas 8 x x 1 dx

Find the mass of the thin bar with the given density function p x 4 if 0 x 3 4 x if 3 x 5 m units Simplify your answer Type an integer or a decimal

11 Consider a cylindrical tank that has a height of 11 m and a radius of 4 m Recall that if the tank is full of water then S 16mpg 15 y dy equals the work required to pump all the water out 0 of the tank through an outflow pipe that is 15 m above the bottom of the tank Revise this work integral for the following scenario Do not evaluate the integrals The work required to empty the tank through an outflow pipe at the top of the tank If D y is the distance a horizontal slice must be lifted what is D y when the outflow pipe is at the top of the tank D y

Why must integration be used to find the work required to pump water out of a tank OA Integration is necessary because the acceleration of gravity changes at each level B Integration is necessary because W mgy O C Water from the same horizontal planes is lifted different distances D Different volumes of water are moved different distances

Find the mass of the thin bar with the given density function 3x 4 p x 1 sin x for 0 x Set up the integral that gives the mass of the thin bar dx Type exact answers

much work is required to move an object from x 2 to x 7 measured in meters with a constant force of 7 N acting along the x axis If a constant force F displaces an object a distance d in the direction of the force what is the correct relationship to use to calculate the work done O A work force distance OB work force distance distance force OD workforce distance OC work

What is the pressure on a horizontal surface with an area of 3 m that is 3 m underwater Use 1000 kg m for the density of water and 9 8 m s for the acceleration due to gravity OOO Points 0 of 1 30 3 1 100 What is the correct relationship to use to find the pressure on the horizontal surface OA pressure pgAh where p is the density of water g is the acceleration due to gravity A is the surface area of the water and h is the depth of the water B pressure pAh where p is the density of water A is the surface area of the water and h is the depth of the water OC pressure pgA where p is the density of water g is the acceleration due to gravity and A is the surface area of the water D pressure pgh where p is the density of water g is the acceleration due to gravity and h is the depth of the water C Sav

35 Bike Tykes is a company that makes bikes for children The company s weekly marginal profit function is given by P x 30x 0 3x 250 dollars per bike when x bikes are sold each week If the company s profit from selling 9 bikes each week is 0 i e the break even quantity is 9 bikes find the company s profit when 80 bikes are sold each week

A sample of argon gas has a volume of 745 mL at a pres sure of 1 30 atm and a temperature of 132 C What is the final volume of the gas in milliliters when the pressure and temperature of the gas sample are changed to the following if the amount of gas does not change 0 55 atm and 81 C Express your answer using two significant figures V VAE

llowing calculate the new temperature in degrees when pressure is changed with n and V constant A tank of helium gas with a pressure of 240 torr at 0 C is heated to give a pressure of 1400 torr Express your answer using two significant figures T Submit Part B AEO Request Answer C A sample of air at 45 0 C and 725 mmHg is cooled to give a pressure of 695 mmHg Express your answer using two significant figures VAE

Sketch the following polar rectangle R 1 0 15r54 50s 1 rs4 Choose the correct graph below QA I 3 FO 61 Q B 61 6 X ww O G OC D Q Q OD 6 3 134

Solve the exponential equation by taking the logarithm of both sides You will need to use a scientific calculator for this problem 5 127 Your answer must be correct to at least 3 decimal places Recall the change of base formula for logarithms log A can be calculated as In A In h

Find the volume of the solid bounded by the surface z f x y and the xy plane Z 52 1 x2 2 y 2 V Type an exact answer using as needed 1 Z 52 1 x y 2

Evaluate the iterated integral rcsc 0 dr d0 JJres R 3 0 rcsc 0 dr d0 Simplify your answer

Draw the solid region whose volume is given by the following double integral Then find the volume of the solid I 01 A 9 dydx V 3 Find the volume of the solid OB OC

Evaluate the following integral x 4 1 x 2 TIT 000 x 4 1 2 ST 000 sin xx sin y sin 4z dy dx dz sin xx sin y sin 4z dy dx dz

Sketch the following region and write an iterated integral of a continuous function f over the region R x y 0 x 2 3x sys 6x 2 x 24 OA 50 OC 3 F Choose the correct iterated integral below OA 2 6x 24 IT 3x P OB f x y dy dx d 50 Q O C OB 50 4 6x 24 OD 6x 24 2 6x 24 Q SO D f x y dx dy f x v dx dv 50 Q

Use a triple integral to find the volume of the solid bounded below by the cone 2 z x y and bounded above by the sphere x y z 288 2 The volume of the solid is 2304 2 3456 cubic units 0 0 288 X 2 y 2 288 z x y

Evaluate the iterated integral J J rcsc0 dr d0 0 2 4

Evaluate the following integral 2 00 0 sin x os y sin z dy dx dz 1 x 2 IT 00 0 Type an exact answer using as needed sin x cos y sin z dy dx dz

Evaluate the following integral as it is written 2x 3 sipx S jx x 4 cos x 2x 3 sip x dy dx dy dx

scuba diver 60 ft below the ocean surface inhales 90 0 mL of ompressed air from a scuba tank at an initial pressure of 3 50 tm and temperature of 9 C Part A What is the final pressure of air in atmo spheres in the lungs when the gas expands to 190 0 mL at a body temperature of 37 C and the amount of gas remai constant P VAEO atm

Use graphical approximation methods to find the point s of intersection of f x and g x f x In x g x 7x The point s of intersection of the graphs of f x and g x is are Type an ordered pair Type integers or decimals rounded to two decimal places as needed Use a comma to sepa answers as needed

Use a graphing utility to find the point s of intersection of f x and g x to two decimal places Note that there are three points of intersection and that is greater than x for large values of x f x ex 5 g x x The intersection points are Type an ordered pair Use a comma to separate answers as needed Round to the nearest hundredth as needed

It x and find the equation of the line tangent to the graph of f at the indicated value of x Find the value s of x where the tangent line is horizontal f x In 12 9x 2x x 1 f x The equation of the line tangent to the graph of f at x 1 is y Select the correct choice below and fill in any answer boxes in your choice OA The value s of x where the tangent line is horizontal is are Simplify your answer Use a comma to separate answers as needed B The tangent line is never horizontal

4 Determine whether the following statements are true and give an explanation or counterexample a When using the shell method the axis of the cylindrical shells is parallel to the axis of revolution b If a region is revolved about the y axis then the shell method must be used c If a region is revolved about the x axis then in principle it is possible to use the disk washer method and integrate with respect to x or the shell method and integrate with respect y a Choose the correct answer below OA False The shell method produces shells that are always perpendicular to the axis of revolution True The shell method always produces shells parallel to the y axis True The rotation of the function about the axis creates a cylindrical shape parallel to the axis OD False The rotation of the function about the axis creates a disk shape perpendicular to the axis B c b Choose the correct answer below OA True Any time a function is revolved about an axis the shell method must be used OB False The shell method can only be used when a region is revolved about the x axis C True Then the axis of the cylindrical shells is parallel to the y axis thod may be used by integration with respect to y

Use the price demand equation below to find E p the elasticity of demand x f p 7200 4p

OA S OB TO Model the situation on a set of axes by placing the center of the base of the cone at the origin and the cone s axis along the positive y axis Set up the integral that gives the volume of the solid using the shell method Use nonnegative and increasing limits of integration Select the correct choice below and fill in the answer boxes to complete your choice Type exact answers dy Volume of the solid formed when a hole of radius 1 is drilled symmetrically along the axis of a right circular cone of radius 6 and height 9 dx Points 0 of 1 CD of 26 points Save

Use both the washer method and the shell method to find the volume of the solid that is generated when the region in the first quadrant bounded by y x about the line x 6 O Set up the integral that gives the volume of the solid as a single integral if possible using the disk washer method Select the correct choice below and fill in any answer boxes within choice Type exact answers OA B 0 0 dx www dy y 25 and x 0 is revolved

a circle of radius 1 centered at 7 0 is revolved about the y axis a Use the shell method to write an integral for the volume of the torus b Use the washer method to write an integral for the volume of the torus c Find the volume of the torus by evaluating one of the two integrals obtained in parts a and b Hint Both integrals can be evaluated without using the Fundamental Theorem of Calculus a Set up the integral that gives the volume of the torus using the shell method Select the correct choice below and fill in the answer boxes to complete your choice Type exact answers O A B S 6 1 dx dy

mine whether the following statements are true and give an explanation or counterexample a When using the shell method the axis of the cylindrical shells is parallel to the axis of revolution b If a region is revolved about the y axis then the shell method must be used c If a region is revolved about the x axis then in principle it is possible to use the disk washer method and integrate with respect to x or the shell method and integrate with respect to y a Choose the correct answer below www OA False The shell method produces shells that are always perpendicular to the axis of revolution OB True The shell method always produces shells parallel to the y axis O C True The rotation of the function about the axis creates a cylindrical shape parallel to the axis O D False The rotation of the function about the axis creates a disk shape perpendicular to the axis O O

the line y 5 SOA S 0 OB 0 Set up the integral that gives the volume of the solid as a single integral if possible using the disk washer method Select the correct choice below and fill in any answer boxes within your choice Type exact answers dx the shell method to find the volume of the solid that is generated when the region in the first quadrant bounded by y x dy Points 0 of 1 GUCCHE Save y 25 and x 0 is revolved

be the region bounded by the following curves Let S be the solid generated when R is revolved about the given axis If possible find the volume of S by both the disk washer and shell methods Check that your results agree y x 2 1 x 0 y 26 revolved about the y axis Set up the integral s that gives the volume of the solid as a single integral if possible using the disk washer method Use increasing limits of integration Select the correct choice below and fill in any answer boxes within your choice OA S OB dy Type exact answers S SO dy dy Type exact answers

regio bounded by y x x 1 and y 0 Use the shell method to find the volume of the solid generated when R is revolved about the line y 3 Set up the integral that gives the volume of the solid using the shell method Use increasing limits of integration Select the correct choice below and fill in the answer boxes to complete your choice Type exact answers OB OA S dy dx

Let R be the region bounded by the following curves Use the shell method to find the volume of the solid generated when R is revolved about the x axis 2 x 2x 0 and y 10 Set up the integral that gives the volume of the solid Use increasing limits of integration Select the correct choice below and fill in the answer boxes to complete your choice Type an exact answer Sody O A OB BETER dx

the region bounded by the following curves Use the shell method to find the volume of the solid generated when R is revolved about the y axis y 13 x y 0 x 1 and x 10 Set up the integral that gives the volume of the solid using the shell method Select the correct choice below and fill in the answer boxes to complete your choice Type exact answers O A O B 1 dy CED dx Sa