Calculus Questions

Use a First and Second Derivative test to identify the Critical Numbers of f x sin x cos x on 0 4 then identify them as either Max s Min s or Neither Make sure to identify where they are by x y Then identify where the point or points of inflection are x y And finally give the intervals of Concavity for the function

Find the derivative y for each curve functo e sx Y x 3x 2

Find each derivative y x 8e 5 y for each given curve

Find each derivative y for each given curve functier 2 y x In x

Find the inverse of matrix A defined by 7 necessary Provide your answer below Use the matrix tool to enter your answer Use fractions whe

Find the derivative y for each curve functice y 2x5 In x 4

You do not need to show work for this question 5 4 3 2 0 2 a List all intervals on which f is increasing b List all r values where f has a local minimum fr c Is f concave up or concave down on 1 x 1 d List all x values where f is not continuous f Is the value of 2 e What is the absolute maximum value of f on 0 4 S z da positive or negative 3 answer to each of th

Sketch one loop of the curve 9y x 3 x Find the area of the surface of revolution generated by one loop of the cum 9y x 3 x about the y axis Leave your answer in the exact form

Use implicit differentiation to find the equation the line which is tangent to the given curve at e point 1 2 xy 3x y 1 2

Given the matrix A 31 7 find det A

Given the matrix A 5 2 4 5 find det A

Since u x 30 then converting back to an expression in x we get the following 23 0 23 2 C 9

Now if u x 30 then 3 x x 30 dx u 2 1 1 du u 2 du x x 3 3 This evaluates as follows Enter your answer in terms of u 13 01 20 du C

If u x 30 is substituted into We must also convert x dx into an expression involving u We know that du x x 30 dx then we have 3x dx so x dx e x x 1 2 dx u x dx du

Consider the following integral te ts dt t8 Find a substitution to rewrite the integrand as 8 U du dt du Evaluate the given integral Use C for the constant of integra

We know that if u f x then du f x dx Therefore if u x 30 then du dx

Use Gaussian elimination to solve the following system of equations 5u 10v 15w 30 2u 9v 14w 103 and 3u8v 4w 13 Select the correct answer below O 3 3 5 O 3 5 3 O 5 3 3 infinitely many solutions Ono solutions

Consider the following integral x5 1 x6 3 dx Given the substitution u x6 3 find du ox dx du Rewrite the given integral in terms of u JC 1 ou Evaluate the integral by making the given substitution Remember to use absolute values where appropriate Use C for the constant of i

Use Newton s method to estimate the two zeros of the following function Start with xo 2 for the left zero and Xo 3 for the right zero Then for each case find x 2x x 4 If x 2 then x Type an integer or a simplified fraction

Consider the following integral Ico Given the substitution u 8x find du du cos 8x dx dx Rewrite the given integral in terms of u SCC 1 du Evaluate the integral by making the given substitution Use C for the constant of integr

The acceleration function in m s2 and the initial velocity are given for a particle moving along a line a t t 4 v 0 3 0 t 11 a Find the velocity at time t v t m s b Find the distance traveled during the given time interval

a Find a power series representation for f x centered at c 0 below b Determine the interval of convergence for the power series 12 7x 3 Enter the interval of convergence for the power series in the space provided f x

Problem 20 Use the method of Lagrange multiplies to minimize f x y z x 4y 22 subject to x 2y z 10

Given that 3 4 2 and 1 2 3 find a u b x Enter the answer to part a in the space provided c the unit vector in the same direction as

Given the following parametric equation x t 3 y 1 6t t for 0 t 4 choose the graph that has the most accurate and complete curve and includes the correct orientation given the limits on t values Be careful here Look closely at the points plotted before making your choice Double check that the orientation is correct Double check endpoints arrows

For the following parametric equation x 3 cos t y 2 sint 1 for t TC Give the value of x and y if t 4 Round the values to the the nearest tenth 1 decimal place Give your answer as an ordered pair x y with no spaces in between symbols For example 17 56

For the following parametric equation x t 1 y 3 2t t Give the value of x and y if t 2 Give your answer as an ordered pair x y with no spaces in between symbols For example 17 56 for 4 t 0

Use substitution to find the indefinite integral 6 fox 5x x ax e dx Sox 6x59x6 dx

Integration by substitution is related to what differentiation method What type of integra Integration by substitution is related to what differentiation method OA Integration by substitution is related to the exponential rule and logarithm rule B Integration by substitution is related to the power rule and quotient rule C Integration by substitution is related to the sum or difference rule D Integration by substitution is related to the chain rule

Use substitution to find the given indefinite integral fx ex 5 ax x 8 8x dx x 8x8 5 dx

Find dy 4 for the equation 2x 4y 1 using implicit differentiation dx

all the local maxima local minima and saddle points of the given function f x y x xy y 3x 3y 6 Select the correct choice below and fill in any answer boxes within your choice OA There are local maxima located at Simplify your answers Type ordered pairs Use a comma to separate answers as needed OB There are no local maxima Select the correct choice below and fill in any answer boxes within your choice OA There are local minima located at Simplify your answers Type ordered pairs Use a comma to separate answers as needed OB There are no local minima Sele e correct choice below and fill in any answer boxes within your choice OA There are saddle points located at Simplify your answers Type ordered pairs Use a comma to separate answers as needed OB There are no saddle points

Given that 3y 3z 12 and 15y 14z 1 solve the system of equations using Gaussian elimination Select the correct answer below 59 55 O 21 59 55 59 infinitely many solutions no solutions

Straight load At time seconds the position of the car in feet is s t 21 Find the average velocity of the car over the time intervals given below a t 10 to t 10 2 seconds b t 10 to t 10 02 seconds c t 10 to 1 10 002 seconds a The average velocity of the car over the time interval from t 10 to t 10 2 seconds moving along a straight road is Simplify your answer Round to one decimal place as needed b The average velocity of the car over the time interval from t 10 to t 10 02 seconds moving along a straight road is Simplify your answer Round to two decimal places as needed c The average velocity of the car over the time interval from t 10 to t 10 002 seconds moving along a straight road is Simplify your answer Round to three decimal places as needed feet sec feet D

Write down the augmented matrix corresponding to the system of equations shown below 6x 5y 4z 7 7x 9y z 7 9x 3y 6z 7 Note Write an equation in each answer field and do not solve the system Provide your answer below

Admission to a movie theater is 7 for children and 11 for adults On a certain day 57 people bought tickets at the theater and 499 was collected How many children s tickets were sold and how many adult s tickets were sold Provide your answer below

Use Gaussian elimination to solve the given system of equations 2m 6n 6 and 8m 15n 3 State the solution as an ordered pair If there are no solutions write

f 5 shirts and 8 sweaters cost 222 and 6 shirts and 5 sweaters cost 202 what is the cost of one shirt and what is the cost of one sweater Provide your answer below

Problem 32 Budgeting for maximum production A manufacturing firm has budgeted 60 000 per month for labor and materials If a thousand is spent on labor and y thousand is spent on materials and if the monthly output in units is given by N x y 4xy 8x then how should the 60 000 be allocated to labor and materials in order to maximize N What is the maximum N

Find the equation of the tangent line to the curve at the given poin 20x xy y 40 at 2 2 The equation of the tangent line is Type an equation Type an exact answer

Problem 30 Use Theorem 2 below to find the local extrema of f x y 2y 6xy x Theorem 2 If 1 z f x y 2 f a b 0 and fy a b 0 3 All second order partial derivatives of exist in some circular region containing a b as center 4 Afrz a b B fay a b C f a b Then Case 1 If AC B 0 and A 0 then f a b is a local maximum Case 2 If AC B 0 and A 0 then f a b is a local minimum Case 3 If AC B 0 then f has a saddle point at a b Case 4 If AC B 0 the test fails

Use the linear equation y x 32 where x is the degrees Fahrenheit and y is the degrees Celsius to convert each terapera a 83 C to Fahrenheit b 93 F to Celsius a 83 C F Round to one decimal place as needed b 93 F C Round to one decimal n

Cantaloupe is given by V The radius is growing at the rate of 0 8 cm week at a time when the radius is 7 5 cm How fast is the volume changing at that moment The volume is changing at a rate of cm week Round to one decimal place as needed

Find f x for the following function Then find f 3 f 0 and f 5 6 f x X f x 0 Select the correct choice below and fill in the answer box within your choice if needed OA f 3 Simplify your answer OB The answer is not a real number OC The answer is undefined Select the correct choice below and fill in the answer box within your choice if needed OA f 0 Simplify your answer OB The answer is not a real number OC The answer is undefined Select the correct choice below and fill in the answer box within your choice if needed OA f 5 Simplify your answer OB The answer is not a real number OC The answer is undefined

Evaluate the integral 2 2 x X 1 2x 8 dx X 1 x 2x 8 Type an integer or decimal rounded to three decimal places as ner dx

Find the equation s of the vertical asymptote s of the given rational function f x X 5 36 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function has two vertical asymptotes The leftmost asymptote is Simplify your answers Type equations OB There is no vertical asymptote OC The function has one vertical asymptote Simplify your answer Type an equation www and the rightmost asymptote

Find the derivative of the following function f x 4x 9 In 3x 2 f x Simplify your answer

expression as a sum and or difference of logarithms with all variables to the first degree In 15w523 In 15w z Type an exact answer in simplified form Use integers or fractions for any numbers in the expression

Problem 88 Revenue and profit functions A company manufactures 10 and 3 speed bicycles The weekly demand and cost functions are p 230 9x y q 130 x 4y C x y 200 80x 30y where p is the price of a 10 speed bicycle q is the price of a 3 speed bicycle x is the weekly demand for 10 speed bicycles y is the weekly demand for 3 speed bicycles and C x y is the cost function Find R 10 5 and Pr 10 5 and interpret the results in words

The scrap value of a machine at the end of its useful life is given by Sin C 1 1 where C is the original cost nis the useful life of the machine in years and r is the constant annual percentage of value lost Find the scrap value of the following machine Onginal cost 68 000 Mife 8 years annual rate of value lost 11 S Round to the nearest cent