Application of derivatives Questions and Answers

Find f 0 for the piece wise function f x 4 x 2 if x 2 X 4 if x 2 f 0

10 84 elect one A Which of the following best expresses angle 0 in terms of h A 0 Arc sin h 169 h 169 34 h 169 h 34 169 B 0 Arc tan C 0 Arctan D 0 Arc tan h 34 169 h 34 169 h 169 h 169 Arc sin Arc tan Arctan Arc tan 34 h 169 8

1744 44 g gallons of fuel was enough energy for the company to assemble p pipes in d days Then 18 more pipes were requested How long would the fuel last now Assume a constant rate of gallons per pipe per day lect one pd g 18 pd p 18 gp 18

13 Evaluate Special Limit C x 2 and Ax 0 05 Evaluate the limit itself not the formula 58 derived from the limit Round to 3 d p Select one 0 322 0 494 2 05 0 685

Help Lecture 63 EX 63 1463 The figure shows the graph of f x x 4x x k Find k TH

Type answer as an a b pair both integers no decimals and no spaces between characters Examples include 2 3 and 5 9 Help Lecture 78 Ex 78 1 1178 If the graph x ay 18 0 intersects y 3x at b 9 find a and b I

9 82 Which of the following equals A 2sin x Select one A D 1 cos2x sin x B sin x C 2cos x D cos x

a the name of the toolkit function in the graph an answer V the equation of the toolkit function in the graph x 10 F x 1 x log x 1 x I x x x x r Irl

Type answer rounded to the nearest rpm For example 200 rpm 1 855 rpm Help Lecture 84 8 What is the rotation rate in rpm of a 20 inch radius tire traveling at 30 ft per seco Round to the nearest rpm 84

17 64 Which of the following is the symbolic form of the graph shown Select one A A f x B f x x x 2 x 3 x 2 x 1 x x 2 x 3 x 2 x 1 x x 2 x 3 x 2 x 1 C f x D f x x 2 x 3 x x 2 x 1

15 Which of the following is the graph of f x tan x 3 x axis tick marks are n 2 radian apart A B Select one A O O D Check B D

Type answer rounded to 1 d p with one space between the number and the units For example 8 8 fps 19 2 fps Help Lecture 84 Ex 84 4 784 If the car s tires had a radius of 1 4 ft and they were rotating at a rate of 50 rpm wh the speed of the car in feet per second fps Round to 1 d p

1473 Which of the following represents the symbolic form of the function shown Select one A A g x x 1 2 C g x 2x B g x x 2 D g x x 2 g x

19 Find the standard form for the equation of a circle whose center is at 2 5 and whos radius is 3 Then expand and write the general form Select one x y 2x 5y 20 0 O x y 4x 10y 29 0 x y 4x 10y 20 0 10y 25 0 O x y 4x

1669 Find the period and phase shift for y 2 5cos2 0 35 Select one period 180 phase shift 35 period 90 phase shift 55 period 180 phase shift 55 period 180 phase shift 55

between the number and the units For example 250 Hz 500 Hz Help Lecture 84 Lesson 84A 84 9 Electricity The voltage was expressed as function of time in seconds by V t 110sin400mt Find the frequency of the voltage fluctuation in Hertz Hz 1 Hz 1 cycle per second Note 1 cycle is the same thing as 1 revolution

453 Given the function k x 0 5x 6x 3 which of the following is true I k has a y intercept at y 6 II k has a zero at x 12 48 III k has a minimum at x 6 B II only A I only elect one A D B C I and II only D I and III only E Ill only

elp Lecture 88 Ex 88 1 88 4 Use upper rectangles with areas equal to f x Ax to estimate the area under the cur f x x on the interval 0 3 Partition the interval into 3 subintervals

The Ettinsmoor Postal Service charges more for boxes whose combined length and girth exceeds 243 mm The length of a package is the length of its longest side the girth is the perimeter of the cross section 2w 2h What is the maximum volume of a package with a square cross section w h that does not exceed the 243 mm standard mm help numbers Maximum volume V

Find the maximum product of two numbers not necessarily integers that have a sum of 386 help numbers

I X A rancher has 768 feet of fencing with which to construct adjacent equally sized rectangular pens as shown in the figure above What dimensions should these pens have to maximize the enclosed area 31 X Maximum area S ft help numbers ft ft

Drug Concentration When a drug is injected into the bloodstream of a patient through the right arm the drug concentration in the bloodstream of the left arm t hours after the injection is approximated by at C t 22 b for some values a and b Lab tests show that those values for Artecoadipine are a 0 29 and b 5 72 for 0 t 24 The model suggests that after injection the drug concentration of Artecoadipine in the left arm is increasing until some time Thours and decreasing afterward Find T Round to 2 decimal places hours

Average Cost Jesaki Water Sports incurs the following costs in producing a water ski vests in one day for 0 x 150 X per vest fixed costs 304 unit production cost 24 per vest equipment maintenance and repairs 0 05 dollars Find the minimum average cost of a water ski vest Round to the nearest cent S LEERDE DE DEUREN Een

Find the Maclaurin polynomials of orders n 0 1 2 3 a Enter the Maclaurin polynomials below for Po x 2 P x 2 2x

D D a ten times the base unit b one tenth of the base u a Ten times the base unit is b One tenth of the base unit is

a the commonly used unit to measu b the commonly used unit to measu c the commonly used unit to measu d the commonly used unit to measu a The commonly used unit to measure b The commonly used unit to measure

Fill in the blank The name commonly used for the Syst me in The name commonly used for the Syst me in

1 Fill in the blanks In the metric system the pre a one thousand times th b one thousandth of the a one thousand times the ba Queandth of the bas

MATH1507 M N rial Assignment My courses SC MATH1507 M N

3 Use the graph of y p x below to find the value to the right 6 5 4 3 2 1 8 7 6 5 3 2 1 0 1 2 3 4

5 4 3 2 1 5 4 3 2 1 2 3 1 2 3 4 The function graphed above is Increasing on the interval s Decreasing on the interval s

Solve the following exponential equation Express irrational solutions in exact form and as a decimal rounded to three decimal places 52 5 6 0 What is the exact answer Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution set is Simplify your answer Type an exact answer B There is no solution

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Select all of the following graphs which repre 1hr11mins X function of x 5 4 3 2 1 2 3 4 5 4 3 2 1 4 3 2 5 4 3 2 1 5 3 1 2 5 4 3 2 1 N 4 5 5 3 1 1 2 3 5 4 3 2 1 2 23 3 4 3 so LO 4 5 4 16

Describe all the numbers that are in the domain of f x 2 4x O x 0 x X Ox 1 2 IV VI 1 2 1 2 x 2 0 x 0 0 x 2 0 x 2 1 2 x 2 All Real Numbe x

Simplify the expression by using sum or difference identities tan tan 1 tan 12 1 tan 12 TO T 12 tan TU 12 tan tan 4 tan T 4 JU 4 I 4

Use log 2 0 376 log 3 0 621 and log 50 778 to approximate the value of the given logarithm to 3 decimal places Assume that b 0 and bz1 Jog 75 X S

Use a double angle formula to find the exact value of the given expression 2 tan 1 tan 2 tan 1 tan 5x 12 Simplify 2 5x 12 25T 12 5x 12

Find the area to three decimal places bounded by f x x e and q x 4 x 7 676 7 333 07 555 07 0

power plant L Z gth underground in miles gth underwater in miles mal cost in dollars offshore facility X ower line is to be run to an offshore facility as shown in the figure above The offshore facility es at sea and L 12 miles along the shoreline from the power plant It costs 450 per mile ver line underground and 700 per mile to run the line underwater D y much of the power line should be run underground and how much underwater to minimize ts help numbers

X X y rancher has 1248 feet of fencing with which to construct adjacent equally siz hown in the figure above What dimensions should these pens have to maximi

Use a graphing calculator to graph the normal probabilit 400 and the standard deviation o 200 Choose the correct graph below A OB

Find real numbers b and c such that f t ebect f t e 3 t What is b b 11

5 In this exercise we investigation the Taylor series of polynomial functions a Find the 3rd order Taylor polynomial centered at a 0 for f x x 2x 3x 1 Does your answer surprise you Explain b Without doing any additional computation find the 4th 12th and 100th order Taylor polynomials centered at a 0 for f x x 2x 3x 1 Why should you expect this c Now suppose f x is a degree m polynomial Completely describe the nth order Taylor polynomial centered at a 0 for each n

1 point Let U Universal set 0 1 2 3 4 5 6 7 8 9 A 0 2 4 5 7 8 and B 0 5 6 8 List the elements of the following sets If there is more than one element write them separated by commas A AUB AUB ANB

1 point Let U Universal set a b c d e 1 2 3 A b c a d 2 and B 3 c e List the elements of the following sets If there is more than one element write them separated by commas AC AUB C AC NBC

1 point The players on a soccer team wear shirts with each player having one of the numbers 1 2 11 on their backs The set A contains players with even numbers on their shirts The set B comprises players wearing an odd number less than 7 The set C contains the defenders which are those wearing numbers less than 6 Select the correct set that corresponds to each of the following Part a ANB U ANC OA 2 4 OB 1 2 3 4 5 OC 2 OD OE 1 3 5 Part b ANB U BNC OA 1 2 3 4 5 6 8 10 OB 2 3 4 5 6 8 10 OC 2 4 6 7 8 9 10 11 OD 6 7 8 9 11 OE 6 7 8 10 11

1 point Consider the universal set U 1 2 3 4 5 6 7 8 9 10 define the set A be the even numbers the set B be the odd numbers and the set C 4 5 10 Complete the following exercises in set notation 1 AUC 2 BOC 3 ANB 4 CC 5 B C Note You may write the empty set as EmptySet

1 point What is the cardinality of each of the following sets a b 0 c 0 mailla lanish d 0 0