Calculus Questions

3 Using the first principals definition of the derivative determine the 1 derivative of the following y KU 2 A 2 2x 3 4 Let f 2 16 f 2 3 g 2 9 and g 2 1 Determine a value for h 2 for the following function h x f x g x A 2 T 2

1 point Find the derivative of the function h x h x BEE 1 1 r5 dr

1 point Find the derivative of the function G x G x 5 cost dt

1 point Find the derivative of the function g r x 16 dx g r

1 point A bacterial colony increases in size at a rate of 4 899e 55t bacteria per hour If the initial population is 88 bacteria find the population 3 hours later Population is bacteria

1 point Find the derivative of the function g x g x 9t 6t dt

8 So 1 point Suppose g x 8 t dt Calculate g x in two different ways Use Part 1 of the Fundamental Theorem of Calculus g x Now differentiate your answer B www Use Part 2 of the Fundamental Theorem of Calculus to evaluate the integral g x BEN

1 point Evaluate the integral 0 3 8x 1 dx

1 point Evaluate the integral 0 20 5 Z dz

1 point Evaluate the integral 2 x 3 1 x 3 dx

1 point Evaluate the integral S 1 3 du 9 1 u 3 u

1 point Evaluate the integral 1 2 14 dt

1 point Evaluate the integral 3x dx

1 point Evaluate the integral 5 Lo 0 y 6 2y 7 dy

1 point Evaluate the integral T 3 T 4 sec x tan x dx

2 1 y dx y c 1 y cosy xydy General Sol

Enonc D terminer les entiers relatifs n tels que n 4 divise 3n 17

Use the general slicing method to find the volume of the following solid TI 2 2 and whose cross sections through the solid perpendicular to the x axis The solid whose base is the region bounded by the curve y 36 cos x and the x axis on are isosceles right triangles with a horizontal leg in the xy plane and a vertical leg above the x axis 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 exact answers OA SO COL dx OB S dy y 36 cos x

Use the general slicing method to find the volume of the following solid The solid whose base is the triangle with vertices 0 0 2 0 and 0 2 and whose cross sections perpendicular to the base and parallel to the y axis are semicircles 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 exact answers O A OB dx dy

Find the area of the region described The region between the line y x and the curve y 2x 25 x in the first quadrant The total area of the shaded region is Type an exact answer

Use the given graph of the function f to answer the following questions Answer Formats Answer Formats Type your answers in interval notation Use INF and INF to denote o and o 5 3 4 2 1 Type your answers in interval notation Use INF and INF to denote 00 and oo Enter NONE if it is not positive negative If there is more than one interval type your answer as a comma separated list For example a b1 az b 2 3 19 Enter NONE if it is not positive negative If there is more than one interval type your answer as a comma separated list For example a b a2 b Part 1 The First Derivative Find the open interval s on which f z is positive negative Type your answers using interval notation 1 f z is positive 2 f z is negative Part 2 The Second Derivative Find the open interval s on which f z is positive negative Type your answers using interval notation 1 f z is positive 2 f 2 is negative

A farmer has 1500 available to build an E shaped fence along a straight river so as to create two identical pastures The materials for the side parallel to the river cost 6 per foot and the materials for the three sections perpendicular to the river cost 5 per foot Find the dimensions for which the total area is as large as possible Dimensions include help units in your answers

Use the given graph of the function f to answer the following questions Answer Formats D 2 Type your answers in interval notation Use INF and INF to denote o and co f x 3 2 2 x Enter NONE if it is not positive negative If there is more than one interval type your answer as a comma separated list For example a1 b1 a b If there is more than one interval type your answer as a comma separated list For example a b a b Part 1 The First Derivative Find the open interval s on which f x is positive negative Type your answers using interval notation 1 f z is positive 2 f z is negative Part 2 The Second Derivative Find the open interval s on which f a is positive negative Type your answers using interval notation 1 f z is positive 2 f z is negative

Find the remaining sides of a 45 45 90 triangle if 49 The shorter sides are each 1 51 The shorter sides are each 4 53 The longest side is 8 2 55 The longest side is 4 50 The shorter sides are each 5 52 The shorter sides are each 54 The longest side is 5V 2 56 The longest side is 12

Distance Figure 19 shows a 75 foot flagpole Use the information in the diagram to work Problems 57 and 58 D 75 ft 60 A FIGURE 19 B A X B 57 a If angle ABC 60 and AB 25 feet find AC b Using part a find AD y 0 G 14 F FIGURE 20 D E

61 Distance a Bullet Travels A bullet is fired into the air at an angle of 45 How far does it travel before it is 1 000 ft above the ground Assume that the bullet travels in a straight line neglect the forces of gravity and give your answer to the nearest foot

The graph on the right gives the annual per person retail availability of beef chicken and pork in Dounds from 2007 to 2012 What is the approximate annual per person retail availability of beef chicken and pork in 2012 The annual per person availability of beef in 2012 is approximately 62 pounds The annual per person availability of chicken in 2012 is approximately 60 pounds The annual per person availability of pork in 2012 is approximately 45 pounds G Points 0 67 of 1 Pounds 70 65 60 55 50 45 40 35 2007 2008 2009 2010 2011 Year

se the revenue and cost graphs on the right to find the approximate cost of manufacturing 8 000 cell phones What is the approximate cost of manufacturing 28 000 phones Dollars in millions 5 4 3 2 1 0 8 Rovenub Cast 16 24 32 40 48

The number of fatalities in coal mines in a certain country for recent years is given in the table below Let x 10 correspond to the year 2010 Sketch the graph of the information in the table Year 2010 2011 2012 2013 2014 2015 2016 Number 43 23 21 21 15 12 7 Choose an appropriate window for the graph The first value on the x axis should be 10 and the last value on the x axis should be 16 Since the maximum y value in the table is 43 the will need to go as high as 45 Sketch the graph Choose the correct answer below OA Coal fatalities 45 04 9 9 Year 16 Q B 45 04 9 9 Year 16 Q O C 45 04 9 9 Year 16 O D 45 0 9 9 Year 16 Q

List the x intercepts and y intercepts of the graph List all the x intercepts Select the correct choice below and if necessary fill in the answer box es to complete your choice A The graph has two x intercepts The leftmost x intercept is 2 5 and the rightmost x intercept is 7 Type integers or decimals B The graph has one x intercept Type an integer or a decimal OC There are no x intercepts List all the y intercepts Select the correct choice below and if necessary fill in the answer box es to complete your choice OA The graph has two y intercepts The bottommost y intercept is topmost y intercept is Type integers or decimals OB The graph has one y intercept Type an integer or a decimal OC There are no v intercepto and the Ay

DETAILS LARMPMT1 10 1 008 Use a protractor to sketch an angle with the given manure a 115

Use the revenue and cost graphs on the right to find the approximate profit from manufacturing 24 000 cell phones What is the approximate profit from manufacturing 24 000 phones Dollars in millions 5 4 3 0 0 Revenue Cast 8 16 24 32 40 Cell phones in thousandel CO 48 G

Find the indefinite integral S 2 I 25 da C

The graph to the right shows the closing share prices in dollars for Company A and Company B on the 21 trading days of the month of January 2018 What was the approximate closing share price for Company A on day 21 Company B The closing share price for Company A on day 21 was 15 5 Round to the nearest ten cents as needed The closing share price for Company B on day 21 was Round to the nearest ten cents as needed 25 24 23 22 A Price 21 M 20 19 18 17 16 15 14 M Company A 25 24 23 Company B 22 21 13 0 2 4 6 8 10 12 14 16 18 20 22 20 19 18 17 16 15 14 400 Day C G E

The following table gives amount of annual spending of a country s defense budget in billions of dollars for military construction Let x 12 correspond to the year 2012 Sketch the graph of the information in the table Year 2012 2013 2014 2015 2016 Spending 11 8 7 8 8 3 5 4 6 9 Choose an appropriate window for the graph The first value on the x axis should be maximum y value in the table is the y axis will need to go as high as and the last value on the x axis should be Since the

Evaluate du Pr u 16 u

2 Using the graph of f x and the definition of continuity a Is the function continuous at x 0 Why or why not b Is the function continuous at x 2 Why or why not c Is the function continuous at x 6 Why or why not f x N 20 3 Consider the function f x X x 6 a Does the Intermediate Value Theorem guarantee a root zero of the function on the interval 0 8 Why or why not b Does the Intermediate Value Theorem guarantee a root zero of the function on the interval 4 0 Why or why not

Use the revenue and cost graphs on the right to find the approximate profit from manufacturing 24 000 cell phones What is the approximate profit from manufacturing 24 000 phones Dollars in millions 5 4 3 1 0 0 Revenue IN Cast 8 16 24 32 40 Cell phones in thousands 48 Q

The graph on the right gives the annual per person retail availability of beef chicken and pork in pounds from 2007 to 2012 What is the approximate annual per person retail availability of beef chicken and pork in 2012 The annual per person availability of beef in 2012 is approximately Pounds 70 65 60 55 50 45 efettalicates 40 35 2007 2008 2009 2010 2011 2012 Year pounds

K The graph to the right shows the closing share prices in dollars for Company A and Company B on the 21 trading days of the month of January 2018 What was the highest closing share price for Company A and on what day did this occur CODE The highest closing share price for Company A was Round to the nearest ten cents as needed on day COD A Price 25 24 23 22 21 20 19 18 17 16 15 14 13 M Company A Q 25 24 Q 23 Serdery B 22 21 20 19 18 17 16 15 14 Day

K 5x 3x 7 0 to solve the equation If the solutions involve square roots give both the exact and approximate solutions B What are the exact solutions Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution s do es not involve s square roots The solution s is are x Simplify your answer Use a comma to separate answers as needed PALAKKA 3 149 10 The solution s involve s square roots The solution s is are x 3 149 10 Type an exact answer using radicals as needed Use a comma to separate answers as needed C There are no real solutions What are the approximate solutions Select the correct choice below and if necessary fill in the answer box to complete your choice A The exact solution s involve s square roots The approximate solution s is are x Round to three decimal places as needed Use a comma to separate answers as needed OB The solution s do es not involve s square roots so there is no approximate solution OC There are no real solutions

Simplify 2 4 2 11 1 16 Type an in That s incorrect Use the quotient rule of exponents m m n x 0

Use the quadratic formula to solve the equation If the solutions involve square roots give both the exact and approximate solutions 5x 3x 7 0 What are the exact solutions Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution s do es not involve s square roots The solution s is are x Simplify your answer Use a comma to separate answers as needed OB The solution s involve s square roots The solution s is are x Type an exact answer using radicals as needed Use a comma to separate answers as needed OC There are no real solutions

Question Determine the following indefinite integral 111 Do not include C in your answer For example if you found the antiderivative was 2t C you would enter 2t 11t7cos t dt

The average annual pay for truckers P in a certain country in thousands of dollars can be approximated by the following function where x represents the number of years since 200 P 0 399x 7 12x 79 4 5 x 15 Find the average annual pay in 2009 Write the expression that can be used to find the average annual pay in 2009 Do not simplify

salon sells its cologne wholesale for 4 75 per bottle The variable costs of producing x thousand bottles is 3x 2420x 325 dollars and the fixed costs for manufacturing are 170 0 Expressions for the revenue cost and profit from selling x thousand items Which expression represents revenue YA R 4750x C R 4 75x Which expression represents cost A C 3x 2420x 169 675 C C 3x 2420x 169 675 Which expression represents profit A P 3x 2330x 169 675 OC p 3x 2330x 169 675 S OB R 4 75x 170 000 OD R 475x OB C 3x 2420x 170 000 OD C 4750x 170 000x O B P 3x 7170x 170 000 OD P 3x 7170x 169 675

Decide whether each solid is a prism pyramid or neither a b c d O O O prism pyramid Oneither prism LARMPMT1 10 4 006 pyramid neither prism pyramid neither Oprism pyramid neither

d expressions for the Revenue Cost and Profit from selling x hundred items tem Price Fixed Costs Variable Costs 5 00 18 000 344x Which expression represents revenue A R 5x 18 000 O C R 5x OB OD F

Shmon factor in the given 7 4y 1 2 3 4y 1 7 4y 1 2 3 4y 1 3 0 Factor completely

Question Find the net signed area between the curve of the function f x 2x 4 and the x axis over the interval 7 3 Do not include any units in your answer Provide your answer below