Calculus Questions

17 1 4x dx A VI 4x C B 1 4r 3 2 C LIN C 1 4x 3 2 C D x 1 4x C 1 VIE E 1 4x C

72 sin 2x 3 dx A cos 2x 3 C B cos 2x 3 C C cos 2x 3 D cos 2x 3 C 1 E cos 2x 3 C

10 If y is implicitly defined by 4 cos x sin y 1 Then y A 1 4 1 1 sin x cos y bb C 1 4 tan x tan y D E tan r tan u B tan x tan y edmuntadt 50 sin y cos x

5 g x x tan x sin x g x A 2x sec x cos x B 2x tan x sin x x 1 1 x 1 1 x C r 3 tan x sin x x sec r cos x D 2x tan x sin x x sec x cos x

3 lim x x x 5 x x HINT Use the conjugate of x x 5 to simplify the expression DAUPHINS A Does not exist B 1 C 0 D 1 2 E 5

7 If g x tan sec x then g x 02 192 A 3 tan secx B 3 tan secx tan x C 3 tan sec x sec I D 3 tan secx sec sec x sec x tan x E 3 tan secx sec sec x sec x

9 If h x x 4 sin x 2 then h x anonton A 2x cos x 2 B 4x2 sin x 2 C 4x cos x 2 D 2x sin x 2 x 4 cos x 2

2 lim sin 4x sin 6x x 0 uds 0 C 0 D 1 E Does not exist A 3 2 B 2 3 C 0

8 If y A x 1 x 1 D then dy OT du dx x 3x 2x 2xx x 1 2x 3x x B x 1 3x2 pex 1 G o x 1 2x 3x x 1 da nat x 1 C ont

4 lim sin x sin x X T

6 If f x 2x43x 9 then f x old xare pul daizs fon 290 A 2x 3x B 8x 6x C 8x 6x 9 D 5

7x4 8x 13x4 16x 1 lim a x 5 A B 0 C 1 D 1 2 E 13

1 2 12 14 Final Sum Factor each completely 1 16x 36x 70 A 2 2x 7 4x 5 B 2 2x 7 4x 5 C 4x 7 2x 5 D 2 4x 7 2x 5 Simplify each expression 2 M 3 A 3 2 2m 1 e LLC All rights 3 3 20

b x 24 2x3 5x2 1 x 2 4 4

You go to the doctor and he gives you 17 milligrams of radioactive dye After 12 minutes 8 milligrams of dye remain in your system To leave the doctor s office you must pass through a radiation detector without sounding the alarm If the detector will sound the alarm if more than 2 milligrams of the dye are in your system how long will your visit to the doctor take assuming you were given the dye as soon as you arrived Give your answer to the nearest minute You will spend minutes at the doctor s office

A wooden artifact from an ancient tomb contains 45 percent of the carbon 14 that is present in living trees How long ago to the nearest year was the artifact made The half life of carbon 14 is 5730 years years Question Help Video Message instructor Submit Question

Question 2 The half life of Radium 226 is 1590 years If a sample contains 300 mg how many mg will remain after 4000 years mg Give your answer accurate to at least 2 decimal places

k x e sin x

X 1 3 4 7 g x 2 1 7 9 C 2 g x 3 8 5 2 Let and gbe inverse functions wheref g 1 The table above gives selected values for g and its derivative g Find f 7 1 8 D

w x cos x 1 sin x 0 T

In x limx 0 sin a limx 2x 1 3x 1 32 22 limx 0x2

x 7 7 x x y

Part III No Calculators Allowed 11 Consider the curve given by 2y2 3xy 2x 12 dy dx a Show that 6x 3y 3x 4y b Is there a horizontal tangent to the curve where x 1 Justify your answer d y c Find at the point 0 6 dr

c x x 1 1 3

8 x9 zx x a 0

s x 3e2ln x 1 4

2 For the following functions find the critical points determine whether each critical point is a local minimum local maximum or neither and provide the global minimum and global maximum on the specified interval 1 2 3 Function f x x 4x 6x 2 g x h x eln x 1 x 3x x 1 Interval 3 5 0

1 Calculate the following limits Use L Hopital s rule if necessary X e x cos x x limx In 1 limx 0 limx 1 sin x x e2 e e e 1 x 1 limx 0 lim 0 cos sin x 1 limx x 4x 3 2x 1

T 13 14 b x 2 24 2x3 5x2 1 x 2 c x x 1 4 4 1 3

3 In the development of a new drug a certain medication concentration in the bloodstream C t measured in miligrams per mililiter is modeled by the function C t 1 50 t 4t 8 where t is the time in hours since the drug was administered How much time does it take for the medication concentration to reach its maximum

4 In a process bacteria are utilized to produce a specific enzyme through fermentation The rate of enzyme production E t measured in units per hour is modeled by the function E t 100t2t where t is the time in hours since the beginning of the fermentation process Determine the time at which the enzyme production is maximized during the process and find the maximum enzyme production rate

14 Given the graph for f has a domain of 2 6 and range of 0 8 Let g x 3f x 2 Find the domain and range of g x

7 Use the graph of f to find the following J a Domain 0 3 3 47 0 4 00 b Zero s 2 points each c Limit Notation of Vertical Asymptote s d End Behavior

5 4 The function f is given by f x x 2x The function g is the result of a transformation of f and is given by g x 2x 4x Which of the following describes the transformation of the graph of f whose image is the graph of g A A vertical dilation by a factor of 2 B A horizontal dilation by a factor of C A vertical dilation by a factor of 2 D A horizontal dilation by a factor of 2 KOBUS The rational function f is given by f x x 3x 1 Which describes the end behavior of f 2x 3 A lim f x and lim f x 8118 x48 o and lim f x X18 B lim f x X118 C lim f x o X118 and lim f x 0 818 IN D lim f x and lim f x 00 8118 X 80

10 275 X

22 tan 945 X

9 455 X

21 sin 150 X

10 275

19 cos 0 1020

os 0 300

17 tan 0 315

13 cos 0 120

1 A conical paper cup 3 inches across the top and 4 inches deep is full of water The cup springs a leak at the bottom and loses water at the rate of 2 cubic inches per minute How fast is the water level dropping at the instant when the water is exactly 3 inches deep Express the answer in inches per minute

2 2 2 d

a 3 points Sketch the graph of f x 2 e by transforming the graph of y e Include any relevant asymptote on your graph 30 y 0 OR X 0

8 4 points The number of bacteria in a culture is increasing according to the law of exponential growth n t noe L of bacterial after 2 5 hours Initially there are 100 bacteria and after 1 hours there are 400 bacteria Find a formula for the number n t nert

5 The length of a solid cylindrical cord of elastic material is 32 inches A circular cross 1 section of the cord has radius inch a What is the volume in cubic inches of the cord

Given the curve x xy 2y 6 a Find an expression for the slope of the curve at any point x y on the curve b Write an equation for the line tangent to the curve at the point 2 1 c Find the coordinates of all other points on this curve with slope equal to the ope at 2 1

4 where Assume that a particle s position on the x axis is given by x 3 cost 4 sint x is measured in feet and t is measured in seconds a Find the particle s position when t 0 t and t 2