Vector Calculus Questions and Answers

stion 5 Write an equation for the quadratic graphed below x intercepts 2 0 and 3 0 y intercept 0 2 2 3 Q

TC 12 0 B olmak zere sec tan ifadesinin e iti nedir 5 ise

Consider the following equation 1000 5 102 Which of the following equations can be used to find the value of t O A log10 1000 5 2t OB log10 200 2t log2 1000 5 10t log 200 10t C D

Find the quotient and remainder using synthetic division xx x x 2 X 2 quotient remainder

Write an algebraic expression that is equivalent to the expression Hint Sketch a right triangle as demonstrated in Example 8 sec arcsin x 1

Use an inverse trigonometric function to write as a function of x 0 0 X 9

Consider the price demand equation given by 8 1 5 2 500 Compute E 1 where E is the elasticity of demand Give your answer to two decimal places Provide your answer below P X

Use the integral test to determine if the series converge or diverge 1 0 2 n 1 n a b 1 n 2 n ln n

Determine whether the series n 0 O B converges or diverges If it converges find its sum Select the correct choice below and if necessary fill in the answer box within your choice OA The series diverges because lim n The series converges because lim n 8 T n T 0 or fails to exist n 0 The sum of the series is Type an exact answer O c The series diverges because it is a geometric series with 21 O D The series converges because it is a geometric series with r 1 The sum of the series is Type an exact answer

2 12 pts Use long division to divide P x by D x and express P in the form P x D x Q x R x Note that this answer is in a different form than that of Problem 1 P x 8x 4x 6 D x 2x 1

quadratic function f is given f x x 14x 35 a Express fin standard form f x b Sketch a graph of f 60 40 20 O 60 40 20 y 60 40 20 20 40 60 y 60 40 20 20 40 60 20 Is this a maximum or minimum value O maximum value minimum value 20 c Find the maximum or minimum value of f f x 40 40 60 60 X X 60 40 60 40 20 20 20 40 60 40 20 40 20 60 20 60 40 60 y y

The graph of f x 5 x 9 2 2 is a parabola that opens downward with its vertex at x y and f 9 is the maximum value of f

The quadratic function f x a x h k is in standard form a The graph of f is a parabola with vertex x y b If a 0 the graph of f opens upward c If a 0 the graph of f opens downward Need Help Read It In this case f h k is the minimum In this case f h k is the maximum v value of f value of f

10 0 y 5 10 b Find the horizontal asymptote Enter None if appropriate 5 10 a Find the vertical asymptote s Separate multiple answers with commas Enter None if appropriate powered by desmos

The price of a home is 170 000 The bank requires a 15 down payment The buyer is offered two mortgage options 15 year fixed at 7 5 or 30 year fixed at 7 5 Calculate the amount of interest paid for each option How much does the buyer save in interest with the 15 year option Use the following formula to determine the regular payment amount PMT P LC nt Find the monthly payment for the 15 year option Round to the nearest dollar as needed MIN

Find the period and the amplitude y 3 cos 4x period amplitude WW 3

The price of a condominium is 89 000 The bank requires a 5 down payment and one point at the time of closing The cost of the condominium is financed with a 30 year fixed rate mortgage at 9 Use the following formula to determine the regular payment amount Complete parts a through e below FA PMT C a Find the required down payment

In terms of paying less in interest which is more economical for a 140 000 mortgage a 30 year fixed rate at 8 or a 15 year fixed rate at 7 5 How much is saved in interest Use the following formula to determine the regular payment amount PMT PA 1 nt Select the correct choice below and fill in the answer box within your choice Do not round until the final answer Then round to the nearest thousand dollars A The 15 year 7 5 loan is more economical The buyer will save approximately OB The 30 year 8 loan is more economical The buyer will save approximately in interest in interest

f x 3 X if x 0 x if x20 a Find the domain of the function b Locate any intercepts c Graph the function d Based on the araph find the range Type your answer in interval notation b Locate any intercepts Select the correct choice below and if necessary fill in the answer box to complete your choice A The intercept s Ware 0 0 3 0 Type an ordered pair Use a comma to separate answers as needed OB There are no intercepts c Choose the correct graph of f x below O A Ay OB o c OU

write O following a 4 1 r down the sequences rezt first three 4 terms of each of the a 3 8 b 1 1 b un S 2 ne zt

The leading term of the polynomial function p x is ax where a is a real number and n is a positive integer The factors of p x include x 3 x 1 xi and x 2 i What is the least possible value of n Justify your answer with appropriate work or an explanation x x 3 x x i x 2 i x x x 3x 3 x 1 x 2 i x x 2x 3 x 2x ix ix 2i 1 x x 2x 3 x 2x 2ix 2 1 x 2x3 21x 2 8 X 26 4x thix 4ix 2x 3x2 bx 6ix bi 3 2 The least is 1 PLX x 3 x 1 x 1 x i x 2 i 2 xx 2x 3 x 1 x 5 2015 7 x 4 8 x 8 2 70 the least is possibi

10 The rate in mg carbon m h at which photosynthesis takes place for a species of phytoplankton is modeled by the function P 100I 1 I 4 where I is the light intensity measured in thousands of foot candles For what light intensity in

4 The sum of two positive numbers is 16 What is the smallest possible value of the sum of their squares

Let f x x 3x and g x 3 x f g x f g x fg x 4 x The domain of f g x is The domain of f g x is The domain of fg x is The domain of x is help formulas help formulas help formulas help formulas help intervals help intervals help intervals help intervals

Let f x 1 x 2 fog x gof x and g x 2 1 X help formulas help formulas

Let f x 5x and g x x 1 f g x f g x fg x 4 The domain of f g x is The domain of f g x is The domain of fg x is The domain of is help formulas help formulas help formulas help formulas help intervals help intervals help intervals help intervals

Let f x 3x 3 and g x 9x 2 fog x gof x fog 4 BI help formulas help formulas help numbers

A function f x has a local maximum if the curve changes from increasing to decreasing O True False

Does the sequence an converge or diverge Find the limit if the sequence is convergent an In n 6 n Select the correct choice below and if necessary fill in the answer box to complete the choice OA The sequence converges to lim an n1x OB The sequence diverges Simplify your answer

Use the formula for the nth term a of a sequence a Find the values of a a2 a3 a4 1 a

Does the sequence a converge or diverge Find the limit if the sequence is convergent an 1 2 Select the correct choice below and if necessary fill in the answer box to complete the choice O A The sequence converges to lim an 81x Type an exact answer OB The sequence diverges

Consider the cost function C x 1x where x is the number of product units If the marginal cost at x 400 units is 100 what is the value of a C x 1 000 ax

c 4 509 793 511 est proche de d 7 108 991 868 est proche de 4 a Estime la valeur de 1 104 886 Je peux arrondir chaque nombre au millier le plus proche 1104 1000 09 886 1000 1 000 1 000 1 104 886 est proche de Effectue l addition pour v rif le r sultat est proche de ton b Estime la valeur de 2 804 12117 O

Let A be an invertible square matrix a What is the column space of A b What is the null space of A

K For the given function find all asymptotes and the coordinates of any holes in its graph 3x 1 f x 5x 12x 9 OA There is one vertical asymptote Its equation is Use integers or fractions for any numbers in the equation B There are two vertical asymptotes The equation of the leftmost one is x 3 and the equation of the 3 rightmost one is x 5 Use integers or fractions for any numbers in the equations OC There are no vertical asymptotes Find the horizontal or oblique asymptotes Select the correct choice below and if necessary fill in the answer box to complete your choice OA The equation of the oblique asymptote is Use integers or fractions for any numbers in the equation OB The equation of the horizontal asymptote is Use integers or fractions for any numbers in the equation 5

domain of f f x 1 5x 3x 3 complete your choice A There is one vertical asymptote Its equation is x 1 Type an equation Use integers or fractions for any numbers in the equation B There are two vertical asymptotes The equation of the leftmost one is rightmost one is Type equations Use integers or fractions for any numbers in the equations OC There are no vertical asymptotes and the equation of the Identify the horizontal or oblique asymptote if one exists Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function has a horizontal asymptote whose equation is Type an equation Use integers or fractions for any numbers in the equation OB The function has an oblique asymptote whose equation is Type an equation in slope intercept form Use integers or fractions for any numbers in the equation C The function has neither a horizontal nor an oblique asymptote

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

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

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

Solve the rational inequality Express your answer in interval notation x 4 x 4 V X X

Suppose that in 1623 a man bought a diamond for 29 Suppose that the man had instead put the 29 in the bank at 3 interest compounded continuously What would that 29 have been worth in 2000 In 2000 the 29 would have been worth Do not round until the final answer Then round to the nearest dollar as needed

A drug is administered intravenously at a constant rate of 7 mg hour and is excreted at a rate proportional to the quantity present with constant of proportionality k 0 a Set up a differential equation for the quantity Q in milligrams of the drug in the body at time t hours Your answer will contain the unknown constants r and k Q 0 b Solve this differential equation assuming there is no drug in the body initially Your answer will contain r and k Q c What is the limiting long run value of Q OG 1

12 Find the quotient Q x and the remainder R x when g x x Find the sum of all the zeros of the polynomial function g x 4x 0

13 Find the horizontal asymptote HA and vertical asymptote VA of x 4 f x x x 2 a HA y 1 b HA y 0 c HA y 1 d HA y 0 e HA None VA x 0 x 2 VA x 0 x 2 VA x 0 VA x 0 VA x 0 x

20 Identify the solution set of the quadratic inequality x 2x 3 0

Find the interval that represents the sotution set to the inequality x 1 3 x 4 Which of the following numbers is not a potential zero of f x 18x 9x 5x 2 3 c d e 2 a 2 b 2 2

7 8 Solve the inequality x26 x Express the solution set in interval notation Solve the inequality x x 2 1

2 If x 2 is a zero of the polynomial function P x 11x 17x 6x3 2 find the sum of the other zeros of the polynomial

8 70 Find the limit Use l Hospital s Rule where appropriate If there is a more elementary method consider using it If l Hospital s Rule doesn t apply explain why X 3 8 lim x 3x 9 9 lim 11 lim x 1 x1 x 1 13 lim 15 lim 1 0 x 2x8 x 4 17 lim 19 lim sin x x 4 tan x 1 e2 1 sin t sin x 1 x1 x x 2 x x 1 e COS X x 8 x 2 x 2 10 lim 12 lim x 4 x 4 tan 3x x 0 sin 2x 14 lim x 2 x x 0 1 cos x 16 lim 1 cos 0 8 1 cos 0 18 lim 20 lim x x x 1 2x

If 380 000 of bonds are issued during the year and 130 000 of bonds are retired during the year the statement of cash flows indirect method will show a n Select one a net decrease in cash of 250 000 in the operating activities section b net increase in cash of 250 000 in the operating activities section c net gain on retirement of bonds of 250 000 in the financing activities section d increase in cash of 380 000 in the financing activities section and a decrease in cash of 130 000 in the financing activities section