Calculus Questions

Tutorial Exercise Find the Maclaurin series for f x using the definition a Maclaurin series Assume that f has a power series expansion Do not show that R x 0 Find the associated radius of convergence R f x 4 1 x

Find the exact length of the curve v 2x 2 0 x 1 3 2 2 1 y X Enhanced Feedback Please try again Remember that the arc length formula for the curve v Fly r ve his

Write the given function as a power series 2 C 1 7 Evaluate the indefinite integral as an infinite series cos x 1 dx cos x 1 1 c

2 Use Stoke s Theorem to evaluate SF d C F x y x 3zsin x x e y cos z S z 1x y z 0 Z

Halo blight is a highly contagious fungus that can spread in some farm crops Five hours after the blight was found 0 46 acres of the field is infected 12 hours later so a total of 17 hours after the blight was found the number of acres infected has grown to 30 7 acres Find the rate at which the blight spreads as a decimal rounded to two decimal places A r Find the number of acres infected when the blight is first identified A Acres The field Is a total of 160 acres Estimate the time for the field to be entirely infected round to the nearest hour

If f x b x 3 for all x write a formula for b n 0 O b O b O b Ob 7 Ob F 7 3 f 3 3 f 3 F 7 7 f 3

b Are these underestimates or overestimates of I L is an underestimate OL is an overestimate OR is an underestimate OR is an overestimate M is an underestimate OM is an overestimate c Use the graph to find T T 45 How does it compare with I T2 I d For any value of n list the numbers L R MT and I in increasing order Enter your answers as a comma separated list Enter your answer using the variables rather than numerical values I T I M Rn n n n x Enhanced Feedback Please try again For finding L R and M use Riemann sums with left endpoints right endpoints and midpoints respectively and let n 2 To find T use a Riemann sum with the mean of the left and right endpoint To list Ln R MT and I graph each one and distinguish between overestimates and underestimates Need Help Bead It Watch It

What area of the brain is responsible for precisely starting stopping or coordinating movements O brain stem motor areas O precommand areas O motor cortex of the cerebrum spinal level Sen

Problem Design the optimal conical container having a cover which hold 0 2m of oil a Find the dimensions r and h of the can that will minimize the cost of the metal to manufacture the container Answers r 0 4070m Height 1 15266m Volume 0 1999m Total area 2 08m b Repeat but without a cover Answers r m h m c Using calculus verify if it is the same as per Excel solver Your excel sheet should have the following format A 1 2 3 4 5 6 7 Radius Height Volume Desired Volume Top area Side area Total area B 2

The adjacent table gives the number of worldwide Internet users in millions Complete parts a through b Year 1995 1996 1997 1998 1999 2000 2001 Users millions 11 39 77 189 292 341 521 Year 2002 2003 2004 2005 2006 2007 Full data se b Use the model to predict the number of users in 2011 million The number of users in 2011 will be approximately Round to the nearest whole number as needed Users millions 589 705 821 1010 1099 1235 a Find the cubic function that is the best fit for the data with y equal to the number of millions of users and x equ the number of years from 1990 y Use integers or decimals for any numbers in the expression Round to three decimal places as needed

4 Evaluate the following 100 4 2 0 2 i 3 i a b 8 2i 3 21 5 2

Use a parameterization to find the flux The flux is SSF n da of F z i xj 22k in the outward direction normal away from the x axis across the surface cut from the parabolic cylinder z 1 y by the planes x 0 x 1 and z 0 S GLOB

Integrate the given function over the given surface G x y z y over the sphere x y 4 Integrate the function SS x y z do S Type an exact answer in terms of T

Using Lagrange multipliers find the min and max distance from the point P 0 1 0 to the ellipsoid 2x y z 6 and also find where the min max distance is attained on the ellipsoid You can assume that the absolute extrema must exist and be attained only at the candidate points determined by Lagrange multipliers

83 Navigation A plane is flying with a bearing of 302 Its speed with respect to the air is 900 kilometers per hour The wind at the plane s altitude is from the southwest at 100 kilometers per hour see figure What is the true direction of the plane and what is its speed with respect to the ground 900 km h W 32 N S E 100 km h 45

Finding a Unit Vector In Exercises 35 36 37 and 38 find the unit vector in the direction of v an verify that it has length 1 35 v 3 12 Answer 17 4 17

Finding a Terminal Point In Exercises 17 and 18 the vector v and its initial point are given Find the terminal point 17 v 1 3 Initial point 4 2 Answer 3 5

a Sketch the given directed line segment b Write the vector in component form c Write the vector as the linear combination of the standard unit vectors i and j d Sketch the vector with its initial point at the origin Initial Point Terminal Point 2 0 5 5 9

Finding Magnitudes In Exercises 39 40 41 and 42 find the following a u b v c u v d e IMI u v u v 39 u 1 1 v 1 2 f

Using the minimum payment balance formula You have a credit card with an APR of 24 The card requires a minimum monthly payment of 5 of the balance You have a balance of 5500 You stop charging and make only the minimum monthl payment What is the balance on the card after three years Enter your answer rounded to the nearest cent

An industrial fan blade rotates 80 times every three minutes If the blade s diameter is 6 ft find the linear and angular velocities of the tip of the blade rounded to the nearest whole number

F x 5 4x3 Describe any relative extrema Select the correct choice below and if necessary fill in the answer box es to within your choice OA The relative minimum point s is are and the relative maximum point s is are Simplify your answers Type ordered pairs using integers or fractions Use a comma to separate answers as needed OB The relative minimum point s is are and there are no relative maximum points Simplify your answer Type an ordered pair using integers or fractions Use a comma to separate answers as needed OC The relative maximum point s is are and there are no relative minimum points Simplify your answer Type an ordered pair using integers or fractions Use a comma to separate answers as needed O D There are no relative minimum points and there are no relative maximum points Identify any intervals over which the function is increasing or decreasing Select the correct choice below and fill in the answer box es within your choice and is not decreasing anywhere or fractions for any numbers in the expression Use a comma to separate answers as needed and decreasing over the interval s OA The function F x is increasing over the interval s Type your answer in interval notation Use integers OB The function F x is increasing over the interval s Type your answers in interval notation Use integers or fractions for any numbers in the expressions Use a comma to separate answers as needed and is not increasing anywhere OC The function F x is decreasing over the interval s Type your answer in interval notation Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed Choose the correct graph below OA 10 Q OB Ay DDD Q O C OD Q Q G

Slope 4 passing through 2 17 What is the point slope form of the equation of the line Simplify your answer Use integers or fractions for any numbers in the equation What is the slope intercept form of the equation of the line Simplify your answer Use integers or fractions for any numbers in the equation Use the figure below to list the slopes m m m3 and m4 in order of decreasing size Use the graph to identify the a x intercept or state that there is no x intercept b y intercept or state that there is no y intercept slope my OA The y intercept is Type an integer OB There is no y intercept slope m slope m slope m Q a Select the correct choice below and fill in any answer boxes within your choice OA The x intercept is Type an integer OB There is no x intercept b Select the correct choice below and fill in any answer boxes within your choice HIDD Choose the correct answer bele O m3 M M M4 m3 M M M4 O m M3 M4 M O m4 M M M3 OOO 10

Which of the following functions grows the LEAST O A c t t 5t OB e t e O c a t t O D g t 3t t E i t In t100

2 f x 4 x OA Select the correct choice below and if necessary fill in the answer box es to complete your choice OA The relative minimum point s is are and the relative maximum point s is are Simplify your answer Use integers or fractions for any numbers in the expression Type an ordered pair Use a comma to separate answers as needed and there are no relative maximum points B The relative minimum point s is are Simplify your answer Use integers or fractions for any numbers in the expression Type an ordered pair Use a comma to separate answers as needed OC The relative maximum point s is are and there are no relative minimum points Simplify your answer Use integers or fractions for any numbers in the expression Type an ordered pair Use a comma to separate answers as needed OD There are no relative minimum points and there are no relative maximum points Choose the correct graph below X Q the function Q O B X CIE 10 Q O C Q Q O D 10

Fill in the table Parent Function Transformed Function a Mapping Notation b Transformation Table c Transformed Graph d Transformed Domain f x 3 g x 2 33 x 1 1 x y

explain the behavior of a tangent line on a curvature y x 1 2 x 4

Write the equation of a sinusoidal graph with the following properties 2 A 3 period 3 flipped over y axis right phase shift TC 4

The current 1 in amperes flowing through a AC alternatice current circuit at time t is 1 220sin 30rt I 6 120 a What is the period b What is the amplitude c What is the phase shift inluding direction

tion 17 Outside temperature over a day can be modeled as a sinusoidal function Suppose you know the temperature is 50 degrees at midnight and the high and low temperature during the day are 57 and 43 degrees respectively Assuming is the number of hours since midnight find an equation for the temperature T in terms of t Work does not need to be shown but provide an explanation in the answer box for full credit

Use the following figure to answer the questions 13 B 54 a 15 C a Solve the triangle b State the area of the triangle

The point 5 11 is on the terminal side of the angle 8 Find the exact value of sec To get full points show your work on your scratch paper

stion 24 A hot air balloon is flying at a height of 152 feet and is directly above Marshall Space Flight Center in Huntsville Alabama THe pilot looks down at the airport which is known to be 5 miles from Marshall Space Flight Center What is the angle of depression in degrees for the baloon to the airport Round to the tenth

The graph of f x 5sin 2 x 1 is obtained from the graph of y sin x by Shifting left 2 units and down 1 unit Stretching vertically by a factor of 2 horizontally by a factor of 5 and down 1 Shifting right 1 unit and up 5 units Vertical stretch by a factor of 5 horizontal shrink by a factor of 2 and a phase shift of 1 unit right Shifting right 5 units and stretching vertically by a factor of 2

Prove the following identity is true 1 cos x cos x sin x 1 tan x full points show your work on yo

4 How do exponential and logarithmic functions relate to each other

H possible 60 30 2 30 this gra 60 90 SI SIXP X 120 150 x

The radius of a wheel rolling on the ground is 78 centimeters If the wheel rotates through an angle of 45 how many centimeters does it move Express your answer in terms of and then round to two decimal places The distance that the wheel moves is centimeters Type an exact answer using as needed Use integers or fractions for any numbers in the expression The distance that the wheel moves is about centimeters Round to two decimal places as needed

To find the distance between two cities a satellite calculates the distances and angle shown not to scale Find the distance between the cities Round answers to the nearest tenth To get full points show your work for this problem on your scratch paper 250 km 1 8 210 km

Find the distance between the pair of points If necessary express answers in simplified radical form and then round to two decimal places 6 1 and 9 5 The distance between the points is units Simplify your answer Type an exact answer using radicals as needed Express the distance rounded to two decimal places if the exact simplified answer contains radicals Select the correct choice below and if necessary fill in the answer box to complete your choice OA The distance between the points is approximately units Type an integer or decimal rounded to two decimal places as needed B The exact simplified form does not contain radicals

The following graph contains the pure form of an 8 Hz cycles per second wave for a time interval of one second What is the period 0 5 0 5 8 O 0 125 2 I 0 2 0 4 X 0 6 0 8

The height in feet of the tide t hours after midnight is modeled in the function in the graph h M 12 20 10 10 20 18 a Is the tide rising or falling at 1 00 AM Be sure to explain b At what time does low tide occur c What is the amplitude of the function and give a practical interpretation of your answer funct and give a practical interpretation of your answer

If tan 0 O 3 5 3 5 O O 4 5 1 2 m 334 and lies in the fourth quadrant then cos 0

The angle of eleveation and depression are always measured from a line prallel to the ground O True False

in x 2 sin x for all values of x True False

Find the measure of ZR to the nearest degree The picture is not neccessarily drawn to scale P 90 145 02 5 7 R 3 Q

Which of the following are the most appropriate equations for the triangle O A 4 C 3 Not drawn to scale 5 3 sin A cos A sin A 3 sin A 2 cos A 4 cos 4 3 sin 4 cos 4 5 B 4 5 3 5 3

Which of the following pairs express the same graph in 20 27 8 x Of x 3sin 20 x g x 3cos 20 f x 3sin 20 g x 3cos 20 f x 3sin 0 8 x 3eus 3cos Of x 3sin 0 x g x 3cos e 2

If the period of a function is 5 9 radians what is it s frequency

What is the reference angle for the angle 163