Calculus Questions

3 For each of the following functions find all values a in o at which the function is discontinuous if there are any At each such value compute the two one sided limits lim f x and x a In x lim f x x and say what type of discontinuity removable discontinuity jump discontinuity vertical asymptote or other occurs at a If there is a removable discontinuity explain how you could redefine the function at that point to make it continuous a h x b g t ln let 4 c f x COS d g x arctan

5 3 2 6 5 4 3 2 1 1234 S 1 2 3 4 5 6 The graph above is a transformation of the function Write an equation for the function graphed above g x

Find a parabola with equation y ax bx c that has slope 14 at x 1 slope 18 at x 1 and passes through the point 2 37 y 9x 4x 9 Need Help X Read It the sewer

Find a cubic function y ax bx2 cx d whose graph has horizontal tangents at the points 2 4 and 2 2 y 3 3 X 10 T 9 4 x 1

Submit Answer 0 07 0 13 Points DETAILS PREVIOUS ANSWERS 7 SCALCET9 3 1 064 At what exact point on the curve y 7 2e 5x is the tangent line parallel to the line 5x

Question 20 Sketch a graph of f x 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 Clear All Draw 1 1 2 2 x2 4 3 4 5 NCY n Question Help Video 1 Video 2 Message instructor

Find the first and second derivative of the function G r r r G r G r 1 2 r H 1 4r 3 1 4 5 57 4 195 257 Enhanced Feedback Please try again using the Power Rule x nx Keep in mind that and The sec

The graph above shows the function f x The graph below shows g x A 2 3 B 11 5 g x is a transformation of f x where g x Af Bx where 3 4

Question 20 Sketch a graph of f x 5 4 3 5 4 3 2 1 Clear All Draw 2 1 1 2 3 4 5 1 12 14 x 2 4 2 2 3 4 5 ANCY

Need Help Submit Answer Read It DETAILS SCALCET9 3 1 067 13 0 13 Points Draw a diagram to show that there are two tangent lines to the parabola of y x that pass through the point 0 16 Find the coordinates of the points where these tangent lines intersect the parabola smaller x value x y

Submit Answer 0 13 Points DETAILS SCALCET9 3 1 074 Find a parabola with equation y ax bx c that has slope 14 at x 1 slope 18 at x 1 and passes through the poi

Sketch a graph of f x 2 x 4 2 5 4 5 4 3 2 1 Clear All Draw 3 2 1 1 2 3 4 5 1 2 3 INOV er 4 5

Differentiate the function 3 1 3 F r F r 9 74

6 54 3 9 4 2 4 q The graph above is a transformation of the function x Write an equation for the function graphed above g x

Find an equation of the tangent line to the curve y x x that is parallel to the line y 3 9x y x 12x 12 X Enhanced Feedback Please try again Find the derivative of the function set it equal to the slope of the given line then solve for x This will give you the x coordinate of the point at which the tangent line is parallel to the find the tangent line Remember that the slopes of two parallel lines are equal and the slope of the line y f a f a x a is f a

The graph of f x 2 is shown in black K Match each transformation c graph below B I 22 1 C 2 2 2 2 K Submit Question R a a red R b green G c blue B Question Help Video Message instructor

ing calculator is recommended ow is the number e defined e is the number such that lim De is the number such that lim Oe is the number such that lim h 00 Oe is the number such that lim h 0 e is the number such that lim im 40 h ho h lim 2 8 1 0 h 2 7 h 1 h 0 99 e h 1 1 1 1 eh eh e h 1 1 h se a calculator to estimate the values of the limits correct to two decima 2 7 1 X 1 1 h X 1 h 0 h 1 1 hat can you conclude about the value of e 0 99 e 1 03 0 99 e 2 7 1 03 e 2 7 2 7 e 2 8 oces1

Find equations of the tangent line and normal line to the curve at the given point y x 7e 0 7 7x 7 tangent line y normal line y 7 7 Enhanced Feedback Please try again The slope of the tangent line at a point is equal to the derivative of the function a ling and the normal line

Solve the initial value problem dy dx 58 xe y 1 e 1

Question 13 Describe a function g x in terms of f x if the graph of g is obtained by reflecting the graph of f about the x axis and if it is horizontally stretched by a factor of 5 when compared to the graph of f g x Af Bx C where A B C

12 Points ifferentiate the function x g x DETAILS 9 5 8x 7 6x SCA

Logistic functions such as N t 500 1 50e 0 13t are often used to model population growth Suppose a population is modeled by this function with time t measured in years Logistic population growth always has a limiting value known as the environmental carrying capacity It is the largest population that the environment can suppor Plot the graph of the population and the line that corresponds to the value of the environmental carrying capacity for this population over the first 80 years Enter expressions in terms of t to graph Separate multiple expressions with commas

Find the interval of convergence for the given power series The series is convergent from x to x left end included Y N right end included Y N 12 1 n x 11 10 n

g x lim x 3x X 3 3 3 3 0 1 3 5x x 1 x 3x 1 x 3 2x 9 x 3 8 The piecewise defined function g is given above Find the following values if possible Show all work a lim g x 3 b lim g x c g 3 x 3 lim xo 35x 3 5 1 3 5 4 cr 2 x 3x 3 2 9 0 L

Homework After a drug is taken orally the amount of the drug in the bloodstream after t hours is f t 118 e 0 4t e t units Complete the following a Graph f t f t and f t in the window 0 12 by 20 75 b How many units of the drug are in the bloodstream after 7 hours c At what rate is the level of drug in the bloodstream increasing after 1 hour d While the level is decreasing when is the level of drug in the bloodstream 10 units e What is the greatest level of drug in the bloodstream and when is this level reached f When is the level of drug in the bloodstream decreasing the fastest a Choose the correct graph below OA Q OB O C D

1 If a b and care unit vectors then la bl2 lb cl2 lc al does not exceed A 4 B 9 C 8 D 6 2 If vectors a 2i k b i j k and c 4i 3j 7k If dx b cx band d a 0 then d will be A 1 Bj 2k B i 8j 2k C 1 8j k D 1 8j 2k Here i j k are unit vectors in the x y and z axis

Find the radius of convergence of the power series Your answer should be a nonnegative real number or INF Radius of convergence is ENG AMBIENT ABRIELE Dements Merancie www BOTH D Pros Entlast MONTH RACHELLES orien naniganty ensarent BALONES AURE ww OBENIAME THREA HARGE MARDARY WEB 22 1 3 26 26

A country that is the major supplier of a certain commodity wishes to improve its balance of trade position by lowering the price of the commodity The demand function is q p a Compute E p b Will the country succeed in raising its revenue a E p Simplify your answer 4000 5

An electronic store can sell q 7 000 p 43 38 cellular phones at a price p dollars per phone The current price is 106 a Is demand elastic or inelastic at p 106 b If the price is lowered slightly will revenue increase or decrease a Is the demand elastic or inelastic at p 106 Type an integer or a decimal rounded to three decimal places as needed OA Inelastic because E p OB Elastic because E p OC Elastic because E p OD Inelastic because E p when p 106 which is greater than 1 when p 106 which is greater than 1 when p 106 which is less than 1 when p 106 which is less than 1

blem 8 Which of the below graphs is an example of a function that satisfies the following conditions g 0 1 g 1 1 g 2 0 g 3 1 g 4 0

t Suppose that the annual sales S in dollars of a company may be approximated empirically by the formula S 30 000 e logarithmic derivative to determine the percentage rate of growth of sales at t 16 The percentage rate of growth is Round to one decimal place as needed C where t is the number of years beyond some fixed reference date Use a

Part 1 of 2 For the demand function below find E p and determine if demand is elastic or inelastic or neither at the indicated price q 400 106 p p 6 E 6 Type an integer or a simplified fraction

mework For the following demand function find E p and determine if demand is elastic or inelastic at the indicated price 800 p 9 q p 19 Part 1 of 2 E 19 Type an integer or a simplified fraction O

Find the present value of 8000 payable at the end of 3 years if money may be invested at 7 with interest compounded continuously The present value of 8000 is Round to the nearest cent as needed

Investment A is currently worth 80 500 and is growing at the rate of 13 per year compounded continuously Investment B is currently worth 70 000 and is growing at the rate of 14 per y compounded continuously After how many years will the two investments have the same value The investments will have the same value after years Do not round until the final answer Then round to the nearest tenth as needed

A famous painting was sold in 1945 for 21 930 In 1993 the painting was sold for 29 5 million What rate of interest compounded continuously did this investment earn As an investment the painting earned an interest rate of Round to one decimal place as needed Points 0 of 1 SILB

Find the present value of 8 000 to be received in 9 years if money may be invested at 5 7 with interest compounded continuously The present value is Round to the nearest cent as needed

Let P t be the population in millions of a certain city t years after 2015 and suppose that P t satisfies the differential equation P t 0 02P t P 0 4 a Use the differential equation to determine how fast the population is growing when it reaches 5 million people b Use the differential equation to determine the population size when it is growing at a rate of 600 000 people per year c Find a formula for P t A Solve 5 0 02P t for P t B Evaluate P t 0 02 5 OC Solve P 5 0 02P t for P t D Evaluate P t 0 02P 5 The population is growing at about 0 1 million people per year when it reaches 5 million people Type an integer or decimal rounded to two decimal places as needed b Choose the correct process to find the population size when it is growing at a rate of 600 000 people per year OA Evaluate P t 0 02P 0 6 B Solve 0 6 0 02P t for P t C Evaluate P t 0 02 0 6 OD Solve P 0 6 0 02P t for P t The population size is about 30 million people when it is growing at a rate of 600 000 people per year Type an integer or decimal rounded to two decimal places as needed c P t

Problem 6 Let f x cos x Which of the following would you use to calculate 2 using the definition of derivative i e first principles A E h 0 h 0 sin 2 h 1 h cos 2 h B lim F lim h 0 sin 2 h h os 2 h C lim h 0 G lim h 0 sin 2 h 1 h sin 2 h h D lim h 0 H lim h 0 cos 2 h 1 cos 2 h 1

g 0 1 g 1 1 g 2 0 g 3 1 g 4 0 B Mit A C 1 0 1 1 0 1 2 X 2 3 3 4 4 5 5 D F 1 0 1 0 1 1 2 X 2 X 3 3 4 4 5

Problem 5 a If an equation of the tangent line to the curve y f x at the point where a 9 is y 10x 2 find 9 and f 9 Problem 5 a Problem 5 b b If the tangent line to y f x at 1 8 passes through the point 7 8 find f 1 and f 1 separate your answers with a comma Your answers MUST be in the correct order Enter your answer symbolically as in these examples separate your answers with a comma MUST the correct order

Problem 4 Suppose that f is continuous on 0 6 and that the only solutions of the equation f x 3 are x 1 and x 5 If f 4 5 then which of the following statements must be true 1 2 3 11 f 0 3 iii f 6 3 A i and iii B ii and iii C iii only D all of them E i only F none of them G i and ii HDG only

2 a Find the horizontal and vertical asymptotes of the graph of the function f x 5x 7 2x 3 h Find the values of a and h for a rational function

4 Suppose that 4 2 g 4 5 f 4 6 and g 4 3 Find derivative 4 in a d a h x 3f x 8g x b h x f x g x c h x d h x f x g x g x f x g x

Find an equation for the tangent line to the curve at the given point Then sketch the curve and the tangent lin together y 223 1 1 2x The equation for the tangent line to the curve is

2 Calculate Brady s yards per attempt YPA YPA Total Passing Yards Total Passing Attempts YPA 79 204 10 598 YPA 7 47 3 Calculate Brady s touchdown percentage TD TD Total Touchdown Passes Total Passing Attempts 100 TD 581 10 598 100 TD 5 48 4 Calculate Brady s interception percentage INT INT Total Interceptions Total Passing Attempts 100 INT 191 10 598 100 INT 1 80 Now use these values to calculate Brady s passer rating using the NFL s formula Passer Rating CMP 30 20 YPA 3 4 TD 20 INT 25 Passer Rating 63 88 30 20 7 47 3 4 5 48 20 1 80 25 Passer Rating 33 88 20 4 47 4 109 6 45 Passer Rating 1 694 1 117 109 6 45 Passer Rating 112 411

17 Distance between Two Ships Two ships leave a port at the same time The first ship sails on a bearing of 40 at 18 knots nautical miles per hour and the second on a bearing of 130 at 26 knots How far apart are they after 1 5 hr

15 Distance Flown by a Plane A plane flies 1 3 hr at 110 mph on a bearing of 38 It then turns and flies 1 5 hr at the same speed on a bearing of 128 How far is the plane from its starting point N 38 N 128

1 Find AC A 118 24 22 B

2 Find AB A C 7 53 44 B