Calculus Questions

Find the volume of a parallelepiped with one of its eight vertices at A 0 0 0 and three adjacent vertices at B 2 3 0 C 0 4 3 and D 3 5 4 The volume of the parallelepiped is Simplify your answer

Write an inequality to describe the following set The slab bounded by the planes y 0 and y 7 planes included The inequality that describes the set of points is Simplify your answer

f x 6 4 y 6 4 2 N 2 X 4 shows the graph of the function

Which of these functions are even OA f x x cos x B f 3 1 csc 3 cos 2x x OC f x OD f x 2 sin x cos x OE f a 1 sec a OF f t sec t

Determine the period for the function y 10 sec 1 x 1 2 10 Type pi for 7 in your answer s if needed Period

Find the length and direction when defined of uxv and vxu u 4i 4j 2k v 2i 2j 4k uxv Type an exact answer using radicals as needed Select the correct choice and fill in any answer boxes in your choice below O A The direction of uxvis i j k Type exact answers using radicals as needed OB The direction of u xv is undefined vxu Type an exact answer using radicals as needed Select the correct choice and fill in any answer boxes in your choice below OA The direction of vxu is i j k Type exact answers using radicals as needed B The direction of vxu is undefined

For the curve determine each of the following Note Use a negative for a shift to the left y 17 tan 7x 2 Period Phase shift

Find parametric equations for the line through 2 5 3 parallel to the x axis Choose the correct answer below OA x 2 y 5 t z 3 t t B x 2 t y 5 z 3 t OC x 2 t y 5 z 3 t OD x 2 y 5 t z 3 t t

dp The marginal price dx at x units of demand per week is proportional to the price p There is no weekly demand at a price of 150 per unit p 0 150 and there is a weekly demand of 7 units at the price of 119 96 per unit p 7 119 96 Use the given information to answer the questions a Find the price demand equation p x Type an exact answer in simplified form Round all decimal values to the nearest hundredth as needed

The weekly marginal cost of producing x pairs of tennis shoes is given by the following function where C x is cost in dollars 200 Xx 1 C x 11 If the fixed costs are 2 000 per week find the cost function What is the average cost per pair of shoes if 1 000 pairs of shoes are produced each week The cost function is C x

Asso W Sketch the region enclosed by the given curves x 1 x3 X 1 x2 0 5 0 5 y 1 0 0 5 0 5 1 0 y 1 0 0 5 0 5 y 0 5 0 5 1 0 1 0 X M 0 5 0 5 1 0 0 5 0 5 1 0 0 5 0 5 y 1 0 0 5 webassign net 0 5 1 0 1 5 1 0 2 0 X X

The weekly marginal revenue from the sale of x pairs of tennis shoes is given by the equation below where R x is revenue in dollars 200 x 1 Find the revenue function Find the revenue from the sale of 1 000 pairs of shoes R x 41 0 03x R 0 0 Find the revenue function R x R x Use integers or decimals for any numbers in the expression

Find the derivative of y with respect to x 12x 3 29 y cos 5 A 12 1 12x 3 2 60 1 12x 3 B 12 25 12x 3 12 25 12x 3 D

t x 9y x 2 7y y 1 0 0 5 0 5 C 4 6 8 0 1 0 F 1 0 0 5 R 8 89 0 5 1 0 M y 1 0 0 5 0 5 1 0 1 0 0 5 webassign net 4 6 0 5 8 1 0

89 M Sketch the region enclosed by the given curves Decide whether to integrate with respect to x or y Draw a typical approximating rectangle 2x y 8 x y 4 2 1 1 2 4 4 2 y 1 C JS Sec

S Sketch the region enclosed by the given curves x 9y x 2 7y y 1 0 0 5 0 5 0 1 0 8 6 WebAssign Plot X M y 1 0 0 5 0 5 1 0 1 0 63 0 5 webassign net 0 5 8 1 0

Classify the graph of the equation as a circle a parabola an ellipse or a hyperbola 9x 25y 15x 250y 543 0 O parabola O ellipse O circle Ohyperbola Submit Answer

E Question 2 7 5 points Ov NEXT 9 2 Domain for f x Range for f x Asymptote for f x End Behavior for f x What function is f x BOOKMARK What function is g x Domain for g 2 Range for g x Asymptote for g a End behavior for g x f z Given that f x and g x are inverses provide the following characteristics 183

Classify the graph of the equation as a circle a parabola an ellipse or a hyperbola x y2 12x 8y 12 0 O parabola O hyperbola O circle O ellipse

Sketch a possible graph of a function f that satisfies the following conditions 1 f x 0 on 5 f x 0 on 5 ii f x 0 on 10 and 10 o f x 0 on 10 10 iii lim f x 3 lim f x 0 24 248 20 18 16 14 12 10 8 8 10 12 14 16 18 20

Consider the function below f x 5x tan x T 2 x 2 a Find the vertical asymptote s Enter your answers as a comma separated list If an answer does not exist enter DNE Find the horizontal asymptote s Enter your answers as a comma separated list If an answer does not exist enter DNE y b Find the interval where the function is increasing Enter your answer using interval notation Find the interval where the function is decreasing Enter your answer using interval notation c Find the local maximum and minimum values If an answer does not exist enter DNE local maximum value local minimum value d Find the interval where the function is concave up Enter your answer using interval notation

Question 10 Find the local minimum and maximum values of the function below f x 3x 12x 108x 6 f x 12x 36x 216x 12x x 6 x 3 From the chart Interval x 3 3 x 0 0 x 6 x 6 12x And f 0 1 T 1 6 x 3 f x T we see that f x changes from negative to positive at 3 so f 3 value by the First Derivative Test Similarly f 2 changes from negative to positive at 6 so f 6 f decreasing on 3 increasing on 3 0 decreasing on 0 6 increasing on 6 is a local minimum is a local minimum value is a local maximum value because f x changes from positive to negative at 0

Sketch the graph of a function that satisfies all of the given conditions f 0 f 2 f 4 0 f x 0 if x 0 or 2 x 4 f x 0 if 0 x 2 or x 4 f x 0 if 1 x 3 f x 0 if x 1 ora 3 2 2 6 2 4

rm is Consider the convergence divergence of the following series whose nth an n 1

Use the graph of f to estimate the values of c that satisfy the conclusion of the Mean Value Theorem fo the interval 0 8 Round your answers to the nearest tenth Enter your answers as a comma separated list C 0 y f x X

Find where the function f x 32 8x 144x 9 is increasing and where it is decreasing 4 2000 4000 6000 8000 4 T 0 6 f x 12x 24x 288x 12x x smallest 0 and largest and arrange To use the I D Test we have to know where f x of the three factors of f x namely 12x x intervals whose endpoints are the critical numbers our work in a chart A plus sign indicates that the given expression is positive and a negative sign indicates that it is negative The last column of the chart gives the conclusion based on the I D Test For instance f x 0 for 0 x 6 so f is Select an answer on 0 6 It would also be true to say that f is decreasing on the closed interval 0 6 Interval HA 4 12x x 6 x 4 f x E x 0 and where f x and a This depends on the signs We divide the real line into f decreasing on 4 Select an answer on 4 0

The graph of the derivative f of a continuous function f is shown Assume the function f is defined only for 0 x 0 y f x 6 a On what interval s is f increasing Enter your answer in interval notation x 8 x On what interval s is f decreasing Enter your answer in interval notation b At what value s of a does f have a local maximum Enter your answers as a comma separated list I At what value s of a does f have a local minimum Enter your answers as a comma separated list c On what interval s is f concave upward Enter your answer in interval notation On what interval s is f concave downward Enter your answer

Consider the function below Use U to denote the union of two intervals f x 4 2x x a Find the interval s of increase Enter your answer using interval notation Find the interval s of decrease Enter your answer using interval notation b Find the local minimum value s Enter your answers as a comma separated list If an answer does not exist enter DNE Find the local maximum value s Enter your answers as a comma separated list If an answer does not exist enter DNE c Find the inflection points x y smaller a value x y larger x value Find the interval s where the graph is concave upward Enter your answer using interval notation Find the interval s where the graph is concave downward Enter un

Find the inflection point of the function Hint g 0 does not exist g x 9x x x g x

Find the points of inflection of the curve y x X X 10 smallest value largest value 1 x 1 x Hint All three lie on one straight line

Suppose the derivative of is x x 2 x 3 x 7 On what interval is f increasing Enter your answer in interval notation

Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval Ente your answers as a comma separated list If an answer does not exist enter DNE f x 0 9 C Graph the function the secant line through the endpoints and the tangent line at c f c 3 2 1 2 16 8 KEN

This exercise uses Newton s Law of Cooling A roasted turkey is taken from an oven when its temperature has reached 185 F and is placed on a table in a room where the temperature is 76 F a If the temperature of the turkey is 150 F after half an hour what is its temperature after 45 min Round your answer to the nearest whole number OF b After how many hours will the turkey cool to 100 F Round your answer to one decimal place hr

A company determines that its marginal revenue per day is given by R t where R t is the total accumulated revenue in dollars on the fth day The company s marginal cost per day is given by C t where C t is the total accumulated cost in dollars on the fth day R t 130e R 0 0 C t 130 0 6t C 0 0 a Find the total profit P T from t 0 to t 10 the first 10 days P T R T C T R t C t dt The total profit is Round to the nearest cent as needed b Find the average daily profit for the first 10 days The average daily profit is Round to the nearest cent as needed

A company determines that its marginal revenue per day is given by R t where R t is the total accumulated revenue in dollars on the th day The company s marginal cost per day is given by C where C t is the total accumulated cost in dollars on the fth day R t 130e R 0 0 C t 130 0 6t C 0 0 a Find the total profit P T from t 0 to t 10 the first 10 days STIR P T R T C T R t C t dt The total profit is Round to the nearest cent as needed b Find the average daily profit for the first 10 days The average daily profit is Round to the nearest cent as needed GUL

The marginal cost in dollars per square foot of installing x square feet of kitchen countertop is given by C x x a Find the cost of installing 50 ft2 of countertop b Find the cost of installing an extra 17 ft2 of countertop after 50 ft2 have already been installed a Set up the integral for the cost of installing 50 ft2 of countertop C 50 dx The cost of installing 50 ft of countertop is Round to the nearest cent as needed b Set up the integral for the cost of installing an extra 17 ft2 after 50 ft has already been installed C 50 17 C 50 dx 50 ELDB The cost of installing an extra 17 ft2 of countertop after 50 ft has already been installed is Round to the nearest cent as needed 4

Find s t where s t represents the position function v t represents the velocity function and a t represents the acceleration function a t 6t 4 with v 0 7 and s 0 5 t SOCIED

Find the area under the graph of f over the interval 2 3 x 1 x 1 2x x 1 f x The area is Simplify your answer

Find the area between the curve and the x axis over the indicated interval y 16 x 4 4 The grounder the sun is Simplify your onewor

This exercise uses the population growth model Some bullfrogs were introduced into a small pond The graph shows the bullfrog population for the next few years Assume that the population grows exponentially 12 A 700 600 500 Frog population 400 300 200 100 0 2 225 1 2 3 a What was the initial bullfrog population bullfrogs 4 5 b Find a function that models the bullfrog population t years since the bullfrogs were put into the pond Round your r value to four decimal places n t c What is the projected bullfrog population after 15 years bullfrogs d Estimate how long it takes the population to reach 124 000 Round your answer to the nearest whole number

Find the average value over the given interval f x x x 8 0 16 The average value of f x x x 8 on 0 16 is Type an integer or a simplified fraction

Explain what the shaded area represents Choose the correct answer below OA The average number of kilowatts used in t hours OB The total number of hours it takes to use t kilowatts OC The total number of kilowatts used in t hours O D The average kilowatts per hour in t hours Number of kilowatts

Find the area of the region bounded by the graphs of the given equations y x 2 y x The area is Type an integer or a simplified fraction

2 12 pts The half life of cesium 137 is 30 years Suppose we have a 10 gram sample a Find a function m t moet that models the mass remaining after t years b Calculate the mass remaining after 50 years Give exact and approximate answers 1 5 grams of the sample remain Give exact and approximate solutions

Instructions Use algebraic techniques to solve problems unless otherwise instructed Show the calculations leading to your answers except basic arithmetic Simplify and circle your final answers 1 12 pts The number of bacteria in a culture was initially 100 and it was 650 after 3 hours a Find a function of the form n t n et that models the number of bacteria after t hours 3r ICD ye 650 ean 13 R IW 3v en 65 6 5 P 3 un 4 5 0 623934059 Ronden 624 b What is the relative growth rate of the population 0 2 62 4 c Calculate the number of bacteria after 12 hours Give exact and approximate answers 100 xe0424x12 178647 5565 178448 d When will the number of bacteria reach 8 000 Give exact and approximate solutions

4 12 pts Based on historical data for population growth rates and the initial number of eagles present in a region biologists expect an eagle population to grow according to the model 200 P t 1 82 33e 0 162t where t is measured in years a How many eagles were initially present b When will the population reach 100 eagles Give exact and approximate solutions

This exercise uses the population growth model The population of the world was 7 1 billion in 2013 and the observed relative growth rate was 1 1 per year a Estimate how long it takes the population to double Round your answer to two decimal places yr b Estimate how long it takes the population to triple Round your answer to two decimal places yr

This exercise uses the radioactive decay model If 250 mg of a radioactive element decays to 240 mg in 48 hours find the half life of the element Round your answer to the nearest whole number hr

Instructions Use algebraic techniques to solve problems unless otherwise instructed Show the calculations leading to your answers except basic arithmetic Simplify and circle your final answers 1 12 pts The number of bacteria in a culture was initially 100 and it was 650 after 3 hours a Find a function of the form n t noe that models the number of bacteria after t hours

Completely factor the following polynomial functions 6 x 16 7 x 2x 24 8 3x 9x 18x