Calculus Questions

The gas law for an ideal gas at absolute temperature T in kelvins pressure P in atmospheres and volume V in liters is PV nRT where n is the number of moles of the gas and R 0 0821 is the gas constant Suppose that at a certain instant P 9 0 a increasing at a rate of 0 15 atm min and V 12 L and is decreasing at a rate of 0 16 L min Find the rate of change of T with respect to time in K min at that instant if n 10 mol Round your answer to four decimal places dT dt K min

Select all that apply DA f x B 1 x c f x 2x 1 X 8 DD f x a graph that does not have a vertical asymptote

domain of f f x 2 X 3 asymptotes for the graph of the rational function State the Identify any vertical asymptotes Select the correct choice below and if necessary fill in the answer box to complete your choice OA There is one vertical asymptote Its equation is Type an equation OB There are two vertical asymptotes The equation of the leftmost one is one is Type equations C There are no vertical asymptotes and the equation of the rightmost

if x y

a lim f x X 2 b lim f x X 0 a Find lim f x or state that it doesn t exist Select the correct choice below and fill in any answer X 2 boxes in your choice OA lim f x X 2 Type an integer OB The limit does not exist b Find lim f x or state that it doesn t exist Select the correct choice below and fill in any answer boxes X 0 in your choice OA lim f x X 0 Type an integer OB The limit does not exist

Consider a generic quadratic function f x ax b c with characteristics described below Determine the domain and range of f The vertex of the graph of is 24 6 a 0 The domain of is The range of f is

Differentiate the function y y In ex xe x

4 Find f 4 if f x 5 6x f 4 Simplify your answer Type an integer or a fraction

Find f g x and g f x f x x 1 g x 12x 5 f g x g f x

In 4 5x find f 0 e 1 25 Enter a number

Differentiate the function f x sin 9 In x I 9 cos 9In x f x cos X

a fog b gof a y ATL Simplify your answer 2 b gof x x 2 Simplify your answer The domain of fog is 4 00 Type your answer in interval notation Use integers or fractions for any numbers in the expression Sir your answer c fof c fof x x 124 42 Simplify your answer d gog The domain of gofis 00 Type your answer in interval notation Use integers or fractions for any numbers in the expression Sim your answer d gog x Simplify your answer The domain off of is 0 00 Type your answer in interval notation Use integers or fractions for any numbers in the expression Simp your answer

J and g given by the following graph 6 2 19 6 8 10 12 Let F z f g z a Find F 1 and F 8 b Use linear approximation to estimate F 0 9 c There are three values of z in 0 10 at which F is not differentiable Find them explain your reasoning

y x8x y x 8e8x ln x 8eln x in x Enhanced Feedback Please try again First take the logarithm on both sides to get an expression for In y Second differenti when logarithmic differentiation is used either the product rule or quotient rule must be applied in the se Need Help Submit Answer 0 12 Points Read It DETAILS Find y if y In 7x 9y Watch It PREVIOUS ANSWERS SCALCET9 3 6 057

Find and simplify the difference quotient f x 7 OA 1 OB 0 O C 1 OD 7 h f x h f x h 11 h 0 for the given function

a fog b gof a fog x x 2 Simplify your answer b gof x x 2 Simplify your answer c fof The domain of fog is 4 00 Type your answer in interval notation Use integers or fractions for any numbers in the expression S your answer d gog c f of x Simplify your answer The domain of g of is 00 Type your answer in interval notation Use integers or fractions for any numbers in the expression S your answer

Find and simplify the difference quotient f x 7x O A O B OC 1 OD O 1 7x x h 1 x x h f x h f x h h 0 for the given functio

Differentiate the function G y 2y 1 G y In 2 y 1 2y 1 4y y 6 2 2 y 1 X

Explain how the graph of the function f x give the domain and range To obtain the graph of f shift the graph of y down Graph the function f x OA 1 x 4 Q X x 4 B 3 can be obtained from the graph of y Then graph fand to the left 4 units reflect across the x axis and shift 3 units 3 Choose the correct graph below Q o o S O D oo S

Let f x cos x sinx a Find the absolute minimum and maximum values of on 0 27 This is asking for the minimum and maximum y values b Find the absolute minimum and maximum values of f on 0 00 Explain Hint How does the graph of f on relate to the graph on 0 27 If you re not sure try graphing the function on a calculator or computer How could you have figured out the behavior without a calculator c Reflect Back Akiko Batari and Carole are working on a All three have found the critical points of f on 0 27 and they have different ideas on what to do next Akiko says I ll use the First Derivative Test Batari says I ll use the Second Derivative Test Carole says I ll plug the critical points and endpoints 0 and 2 into f to see which have the highest and lowest values of f those are the absolute maximum and absolute minimum Do all three have complete plans or might they need to do more work beyond what they said liko best and why

Find y and y y In sec 2x tan 2x y 2 sec 2x X y 4 sec 2x tan 2x X

Use the graphs of the rational functions in A to D on the right to answer the question Give all possible answers as there may be more than one correct choice Which choices have the x axis as a horizontal asymptote Select all the graphs that apply Graph C Graph B Graph D Graph A B C D Q 18 18 1 H Q Z

For f x x 3 and g x 4 x find a fog x b the domain of fog a fog x x 7 Simplify your answer b What is the domain of f o g The domain is Simplify your answer Type your answer in interval notation Use integers or fractions for any numbers in the e

6 A car has a 16 gallon fuel tank When driven on a highway it has a gas mileage of 30 miles per gallon The gas mileage also called fuel efficiency tells us the number of miles the car can travel for a particular amount of fuel one gallon of gasoline in this case After filling the gas tank the driver got on a highway and drove for a while a How many miles has the car traveled if it has the following amounts of gas left in the tank i 15 gallons ii 10 gallons iii 2 5 gallons b Write an equation that represents the relationship between the distance the car has traveled in miles d and the amount of gas left in the tank in gallons c How many gallons are left in the tank when the car has traveled the following distances on the highway i 90 miles ii 246 miles d Write an equation that makes it easier to find the amount of gas left in the tank I if we know the car has traveled d miles

lain how the graph of the function f x 2 can be obtained from the graph of y Then graph f and give main and range To obtain the graph of f shift the graph of y SLEER up to the left unit s to the right down

Charlotte Mecklenburg Schools 7 Noah is helping to collect the entry fees at his school s sports game Student entry costs 2 75 each and adult entry costs 5 25 each At the end of the game Diego collected 281 25 Select all equations that could represent the relationship between the number of students s the number of adults a and the dollar amount received at the game a 281 255 25a 2 75s 281 25 2 758 5 25 b a c 281 25 5 25s a d 281 25 2 75a s e 281 25 5 25s a

What is the largest open interval over which f x increases decreases and is constant What is the largest open interval over which f x increases Select the correct choice below and if necessary fill in the answer box to complete your choice OA The open interval is Type your answer in interval notation Use a comma to separate answers as needed B None What is the largest open interval over which f x decreases Select the correct choice below and if necessary fill in the answer box to complete your choice The open interval s is are Type your answer in interval notation Use a comma to separate answers as needed B None OA

What is the equation of the vertical asymptote of the graph of y horizontal asymptote 1 What is the vertical asymptote of the graph of y X 4 The equation of the vertical asymptote is x 5 1 X 4 5 What is the equation of the

Find the dimensions of the rectangle with perimeter 1360 centimeters and maximum area length width area centimeters centimeters What is the maximum area square centimeters

feet of fencing find the dimensions that maximize the area of the pen using all of the available fencing material Pen 1 Let w be the width of the enclosure and let l be the length of the enclosure as shown above Write an function for the area A of the enclosure in terms of w A w What width w and length I would maximize the area W Barn W ft and l What is the maximum area square feet feet W

What is the domain of x What is its range The domain of f x Type your answer in interval notation

K For f x a fog 6 X 5 Type your answer in interval notation Use integers or tractions for any numbers in the expression Sim your answer 5 and g x find the following composite functions and state the domain of each X b gof c fof d gog 5X 25 6 Simplify your answer Use integers or fractions for any numbers in the expression b gof x The domain of gofis 5 U 5 00 Type your answer in interval notation Use integers or fractions for any numbers in the expression Sin your answer 6 x 5 31 5x Simplify your answer Use integers or fractions for any numbers in the expression c f of x 31 31 7 51 0 5 The domain off of is o 5 U 5 Type your answer in interval notation Use integers or fractions for any numbers in the expression Sir your answer d gog x Simplify your answer Use integers or fractions for any numbers in the expression

5 The area A of a rectangle is represented by the formula A lw where I is the length and w is the width The length of the rectangle is 5 Write an equation that makes it easy to find the width of the rectangle if we know the area and the length

Determine the slope of the tangent to the graph at x 4 Determine Y 8 dy dx for Determine the slope of the tangent to the graph at x 4 0 y 16x 13 Given that f x lim f x h f x h h 0 Y Give answers rounded to two decimal places 12 5 Determine the slope of the tangent to the graph at x 5 5 X when x 6 11 22 y 5x4 x 1 for all x evaluate Determine the equation of the tangent line to the curve at point 1 6 y x 5x 2x

The derivative of a function f in terms of a limit is defined by which of the following lim f x h f x h 0 h lim x h lim f h f r h h 0 lim lim h 0 f x h f x h Determine Determine f x f a a y 3x 18 5 dy dr dy dr fi 0 for What value is the following limit calculating 4 h 4 for fi 4 for f x x fi 16 for f x x fi 4 for f x x f a A y 732

Find equations of the tangent lines to the curve y at the point 1 0 nt at the pointe y 7 In x X Illustrate by graphing the curve and its tangent lines e at the points 1 0 ande

A curve passes through the point 0 7 and has the property that the slope of the curve at every point P is twice the y coordinat of P What is the equation of the curve Use x as the independent variable y x

A fireplace arch is to be constructed in the form of a semiellipse The opening is to have a height of 3 feet at the center and a width of 8 feet along the base The contractor cuts a string of a certain length and nails each end of the string at the foci of the base in order to sketch the outline of the semiellipse a What is the total length of the string Select b How far from the center should the string be nailed into the base Select

Find y and y y y y In x 8 x

Differentiate the function F t F t In 5t 1 4 2t 1 5

If f x In 4 e5x find f 0 f 0

Find y and y y y y In sec 2x tan 2x

Convert general form to standard form General form 4x 9y 48x 72y 144 0 y k E Standard form h k D E x h D 1

A satellite dish is the shape of a paraboloid The dish is 38 inches wide and 10 inches deep How many inches should the receiver be located from the vertex for optimal reception round to the nearest thousandth Receiver

Determine the location of the focus and the directrix of the parabola y 6y 8x 23 0 Focus Select Directrix Select Select

Perform the subtraction and find the difference 2x 0x 12x 2x 8x 6x Ax Bx A type your answer B type your answer

The annual consumption of beef per person was about 64 5 lb in 2000 and about 60 3 lb in 2008 Assume B t the annual beef consumption t years after 2000 is decreasing according to the exponentia decay model a Find the value of k and write the equation b Estimate the consumption of beef in 2010 c In what year theoretically will the consumption of beef be 20 lb a Select the correct answer below and fill in the answer box to complete your choice Round to four decimal places as needed 60 3 O A O C B t B t 64 5 60 3e OB B t 64 5e OD B t 60 3e

Select all the correct answers Which statements are true about function g g x 000 www 9x 27x 25 2 x 2 Function g is increasing over the entire domain Function g includes an exponential piece and a quadratic piece As x approaches positive infinity g x approaches positive infinity Function g is continuous As x approaches negative infinity g x approaches positive infinity

Let f x x x Find f 4

Problem 1 Find the value of y when x 0 if xy ey 7 e