Precalculus Enhanced with Graphing Utilities (7th Edition)
7th Edition
ISBN: 9780134119281
Author: Michael Sullivan, Michael Sullivan III
Publisher: PEARSON
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Chapter 3.5, Problem 20SB
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4. Find the inverse Laplace Transform Show all of your work:
a. F(s) =
=
2s-3
(s²-10s+61)(5-3)
se-2s
b. G(s) =
(s+2)²
1. Consider the differential equation, show all of your work:
dy
=(y2)(y+1)
dx
a. Determine the equilibrium solutions for the differential equation.
b. Where is the differential equation increasing or decreasing?
c. Where are the changes in concavity?
d. Suppose that y(0)=0, what is the value of y as t goes to infinity?
2. Suppose a LC circuit has the following differential equation:
q'+4q=6etcos 4t, q(0) = 1
a. Find the function for q(t), use any method that we have studied in the course.
b. What is the transient and the steady-state of the circuit?
Chapter 3 Solutions
Precalculus Enhanced with Graphing Utilities (7th Edition)
Ch. 3.1 - Graph y=2x3 . (pp. 32-35)Ch. 3.1 - Find the slope of the line joining the points (...Ch. 3.1 - Find the average rate of change of f(x)=3 x 2 2 ,...Ch. 3.1 - Solve: 6x900=15x+2850 . (pp. A44-A46)Ch. 3.1 - If f( x )= x 2 4 , find f( 2 ) . (pp. 60-62)Ch. 3.1 - True or False The graph of the function f( x )= x...Ch. 3.1 - For the graph of the linear function f( x )=mx+b ,...Ch. 3.1 - If the slope m of the graph of a linear function...Ch. 3.1 - True or False The slope of a nonvertical line is...Ch. 3.1 - True or False The average rate of change of f( x...
Ch. 3.1 - What is the only type of function that has a...Ch. 3.1 - A car has 12,500 miles on its odometer. Say the...Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 13-20, a linear function is given. a....Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - In Problems 21-28, determine whether the given...Ch. 3.1 - Suppose that f( x )=4x1 and g(x)=2x+5 . a. Solve...Ch. 3.1 - Suppose that f( x )=3x+5 and g(x)=2x+15 . a. Solve...Ch. 3.1 - In parts (a) - (f), use the following figure. a....Ch. 3.1 - In parts (a) - (f), use the following figure. a....Ch. 3.1 - In parts (a) and (b), use the following figure. a....Ch. 3.1 - In parts (a) and (b), use the following figure. a....Ch. 3.1 - In parts (a) and (b), use the following figure. a....Ch. 3.1 - In parts (a) and (b), use the following figure. a....Ch. 3.1 - Car Rentals The cost C , in dollars, of a one-day...Ch. 3.1 - Phone Charges The monthly cost C , in dollars, for...Ch. 3.1 - Supply and Demand Suppose that the quantity...Ch. 3.1 - Supply and Demand Suppose that the quantity...Ch. 3.1 - Taxes The function T( x )=0.15(x9225)+922.50...Ch. 3.1 - Competitive Balance Tax In 2011, major league...Ch. 3.1 - The point at which a company’s profits equal...Ch. 3.1 - The point at which a company’s profits equal...Ch. 3.1 - Straight-line Depreciation Suppose that a company...Ch. 3.1 - Straight-line Depreciation Suppose that a company...Ch. 3.1 - Cost Function The simplest cost function is the...Ch. 3.1 - Cost Function Refer to Problem 47. Suppose that...Ch. 3.1 - Truck Rentals A truck rental company rents a truck...Ch. 3.1 - International Calling A cell phone company offers...Ch. 3.1 - Developing a Linear Model from Data How many songs...Ch. 3.1 - Developing a Linear Model from Data The following...Ch. 3.1 - Which of the following functions might have the...Ch. 3.1 - Which of the following functions might have the...Ch. 3.1 - Under what circumstances is a linear function f( x...Ch. 3.1 - Explain how the graph of f( x )=mx+b can be used...Ch. 3.1 - Problems 57-60 are based on material teamed...Ch. 3.1 - Problems 57-60 are based on material teamed...Ch. 3.1 - Problems 57-60 are based on material teamed...Ch. 3.1 - Problems 57-60 are based on material teamed...Ch. 3.2 - Plot the points ( 1,5 ),( 2,6 ),( 3,9 ),( 1,12 )...Ch. 3.2 - Find an equation of the line containing the points...Ch. 3.2 - A _____________ is used to help us to see what...Ch. 3.2 - If the Independent variable in a line of best fit...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 5-10, examine the scatter diagram and...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - In Problems 11-16, (a) Draw a scatter diagram. (b)...Ch. 3.2 - Candy The following data represent the weight (in...Ch. 3.2 - Tornadoes The following data represent the width...Ch. 3.2 - Video Games and Grade-Point Average Professor...Ch. 3.2 - Hurricanes The following data represent the...Ch. 3.2 - Homeruns A baseball analyst wishes to find a...Ch. 3.2 - Demand for Jeans The marketing manager at...Ch. 3.2 - Maternal Age versus Down Syndrome A biologist...Ch. 3.2 - Find the line of best fit for the ordered pairs (...Ch. 3.2 - What does a correlation coefficient of 0 imply?Ch. 3.2 - Explain why it does not make sense to interpret...Ch. 3.2 - Refer to Problem 19. Solve G( h )=0 . Provide an...Ch. 3.2 - Find an equation for the line containing the...Ch. 3.2 - Find the domain of f( x )= x1 x 2 25 .Ch. 3.2 - For f(x)=5x8 and g(x)= x 2 3x+4 , find (gf)(x) .Ch. 3.2 - Write the function whose graph is the graph of y=...Ch. 3.3 - List the intercepts of the equation y= x 2 9 ....Ch. 3.3 - Prob. 2AYPCh. 3.3 - To complete the square of x 2 5x , you add the...Ch. 3.3 - To graph y= (x4) 2 you shift the graph of y= x 2...Ch. 3.3 - The graph of a quadratic function is called a(n)...Ch. 3.3 - The vertical line passing through the vertex of a...Ch. 3.3 - The x-coordinate of the vertex of f( x )=a x 2...Ch. 3.3 - True or False The graph of f( x )=2 x 2 +3x4 opens...Ch. 3.3 - True or False The y-coordinate of the vertex of f(...Ch. 3.3 - True or False If the discriminant b 2 4ac=0 , the...Ch. 3.3 - If b 2 4ac0 , which of the following conclusions...Ch. 3.3 - If the graph of f( x )=a x 2 +bx+c,a0 , has a...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 13-20, match each graph to one the...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 21-32, graph the function f by...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 33-48, (a) graph each quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 49-54, determine the quadratic...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems 55-62, determine, without graphing,...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - In Problems 63-74, (a) graph each function, (b)...Ch. 3.3 - The graph of the function f( x )=a x 2 +bx+c has...Ch. 3.3 - The graph of the function f(x)=a x 2 +bx+c has...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - In Problems 77-82, for the given functions fandg ,...Ch. 3.3 - Answer Problems 83 and 84 using the following: A...Ch. 3.3 - Answer Problems 83 and 84 using the following: A...Ch. 3.3 - Suppose that f(x)= x 2 +4x21 . (a) What is the...Ch. 3.3 - Suppose that f( x )= x 2 +2x8 . (a) What is the...Ch. 3.3 - Find the point on the line y=x that is closest to...Ch. 3.3 - Find the point on the line y=x+1 that is closest...Ch. 3.3 - Maximizing Revenue Suppose that the manufacturer...Ch. 3.3 - Maximizing Revenue The John Deere company has...Ch. 3.3 - Minimizing Marginal Cost The marginal cost of a...Ch. 3.3 - Minimizing Marginal Cost (See Problem 91.) The...Ch. 3.3 - Business The monthly revenue R achieved by selling...Ch. 3.3 - Business The daily revenue R achieved by selling x...Ch. 3.3 - Stopping Distance An accepted relationship between...Ch. 3.3 - Birthrate for Unmarried Women In the United...Ch. 3.3 - Let f( x )=a x 2 +bx+c , where a,b,andc are odd...Ch. 3.3 - Make up a quadratic function that opens down and...Ch. 3.3 - On one set of coordinate axes, graph the family of...Ch. 3.3 - On one set of coordinate axes, graph the family of...Ch. 3.3 - State the circumstances that cause the graph of a...Ch. 3.3 - Why does the graph of a quadratic function open up...Ch. 3.3 - Can a quadratic function have a range of ( , ) ?...Ch. 3.3 - What are the possibilities for the number of times...Ch. 3.3 - Determine whether x 2 +4 y 2 =16 is symmetric...Ch. 3.3 - Find the domain of f(x)= 82x .Ch. 3.3 - Prob. 107RYKCh. 3.3 - Write the function whose graph is the graph of y=...Ch. 3.4 - Translate the following sentence into a...Ch. 3.4 - Use a graphing utility to find the line of best...Ch. 3.4 - Maximizing Revenue The price p (in dollars) and...Ch. 3.4 - Maximizing Revenue The price p (in dollars) and...Ch. 3.4 - Maximizing Revenue The price p (in dollars) and...Ch. 3.4 - Maximizing Revenue The price p (in dollars) and...Ch. 3.4 - Enclosing a Rectangular Field David has 400 yards...Ch. 3.4 - Enclosing a Rectangular Field Beth has 3000 feet...Ch. 3.4 - Enclosing a Rectangular Field with a Fence A...Ch. 3.4 - Enclosing a Rectangular Field with a Fence A...Ch. 3.4 - Analyzing the Motion of a Projectile A projectile...Ch. 3.4 - Analyzing the Motion of a Projectile A projectile...Ch. 3.4 - Suspension Bridge A suspension bridge with weight...Ch. 3.4 - Architecture A parabolic arch has a span of 120...Ch. 3.4 - Constructing Rain Gutters A rain gutter is to be...Ch. 3.4 - Norman Windows A Norman window has the shape of a...Ch. 3.4 - Constructing a Stadium A track-and-field playing...Ch. 3.4 - Architecture A special window has the shape of a...Ch. 3.4 - Chemical Reactions A self-catalytic chemical...Ch. 3.4 - Calculus: Simpson's Rule The figure shows the...Ch. 3.4 - Use the result obtained in Problem 20 to find the...Ch. 3.4 - Use the result obtained in Problem 20 to find the...Ch. 3.4 - Use the result obtained in Problem 20 to find the...Ch. 3.4 - Use the result obtained in Problem 20 to find the...Ch. 3.4 - Life Cycle Hypothesis An individuals income varies...Ch. 3.4 - Height of a Rail A shot-putter throws a hall at an...Ch. 3.4 - Which Model? The following data represent the...Ch. 3.4 - Which Model? An engineer collects the following...Ch. 3.4 - Which Model? The following data represent the...Ch. 3.4 - Which Model? A cricket makes a chirping noise by...Ch. 3.4 - Refer to Example 1 in this section. Notice that if...Ch. 3.4 - Find an equation of the line containing the points...Ch. 3.4 - Find the distance between the points P 1 =( 4,7 )...Ch. 3.4 - Prob. 34RYKCh. 3.4 - Find the intercepts of the graph of 3 x 2 4y=48 .Ch. 3.5 - Solve the inequality 3x27 .Ch. 3.5 - Write (2,7] using inequality notation.Ch. 3.5 - (a) f( x )0 (b) f( x )0Ch. 3.5 - (a) g( x )0 (b) g( x )0Ch. 3.5 - (a) g( x )f( x ) (b) f( x )g( x )Ch. 3.5 - (a) f( x )g( x ) (b) f( x )g( x )Ch. 3.5 - x 2 3x100Ch. 3.5 - x 2 +3x100Ch. 3.5 - x 2 4x0Ch. 3.5 - x 2 +8x0Ch. 3.5 - x 2 90Ch. 3.5 - x 2 10Ch. 3.5 - x 2 +x12Ch. 3.5 - x 2 +7x12Ch. 3.5 - 2 x 2 5x+3Ch. 3.5 - 6 x 2 6+5xCh. 3.5 - x 2 x+10Ch. 3.5 - x 2 +2x+40Ch. 3.5 - 4 x 2 +96xCh. 3.5 - 25 x 2 +1640xCh. 3.5 - 6( x 2 1 )5xCh. 3.5 - 2( 2 x 2 3x )9Ch. 3.5 - What is the domain of the function f( x )= x 2 16...Ch. 3.5 - What is the domain of the function f( x )= x3 x 2...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - In Problems 25-32, use the given functions f and g...Ch. 3.5 - Physics A ball is thrown vertically upward with an...Ch. 3.5 - Physics A ball is thrown vertically upward with an...Ch. 3.5 - Revenue Suppose that the manufacturer of a gas...Ch. 3.5 - Revenue The John Deere company has found that the...Ch. 3.5 - Artillery A projectile Fired from the point ( 0,0...Ch. 3.5 - Runaway Car Using Hooke's Law, we can show that...Ch. 3.5 - Show that the inequality ( x4 ) 2 0 has exactly...Ch. 3.5 - Show that the inequality ( x2 ) 2 0 has one real...Ch. 3.5 - Explain why the inequality x 2 +x+10 has all real...Ch. 3.5 - Explain why the inequality x 2 x+10 has the empty...Ch. 3.5 - Explain the circumstances under which the...Ch. 3.5 - Determine the domain of f( x )= 102x .Ch. 3.5 - Consider the linear function f( x )= 2 3 x6 . (a)...Ch. 3.5 - Determine algebraically whether f( x )= x x 2 +9...Ch. 3.5 - Determine whether the graphs of 6x3y=10 and 2x+y=8...Ch. 3.R - In Problems 1-3: (a) Determine the slope and...Ch. 3.R - In Problems 1-3: (a) Determine the slope and...Ch. 3.R - In Problems 1-3: (a) Determine the slope and...Ch. 3.R - In Problems 4 and 5, determine whether the...Ch. 3.R - In Problems 4 and 5, determine whether the...Ch. 3.R - In Problems 6-8, graph each quadratic function...Ch. 3.R - In Problems 6-8, graph each quadratic function...Ch. 3.R - In Problems 6-8, graph each quadratic function...Ch. 3.R - In Problems 9-14, (a) graph each quadratic...Ch. 3.R - In Problems 9-14, (a) graph each quadratic...Ch. 3.R - In Problems 9-14, (a) graph each quadratic...Ch. 3.R - In Problems 9-14, (a) graph each quadratic...Ch. 3.R - In Problems 9-14, (a) graph each quadratic...Ch. 3.R - In Problems 9-14, (a) graph each quadratic...Ch. 3.R - In Problems 15-17, determine whether the given...Ch. 3.R - In Problems 15-17, determine whether the given...Ch. 3.R - In Problems 15-17, determine whether the given...Ch. 3.R - In Problems 18-19, solve each quadratic...Ch. 3.R - In Problems 18-19, solve each quadratic...Ch. 3.R - 20. In Problems 20 and 21, find the quadratic...Ch. 3.R - 21. In Problems 20 and 21, find the quadratic...Ch. 3.R - 22. Sales Commissions Bill has just been offered a...Ch. 3.R - 23. Demand Equation the price p (in dollars) and...Ch. 3.R - 24. Enclosing the Most Area with a Fence A farmer...Ch. 3.R - 25. Minimizing Marginal Cost Callaway Golf Company...Ch. 3.R - 26. Maximizing Area A rectangle has one vertex on...Ch. 3.R - 27. Parabolic Arch Bridge A horizontal bridge is...Ch. 3.R - 28. Bono Length Research performed at NASA, led by...Ch. 3.R - 29. Advertising A small manufacturing firm...Ch. 3.CT - For the linear function f( x )=4x+3 , a. Find the...Ch. 3.CT - Determine whether the given function is linear or...Ch. 3.CT - Graph f(x)= (x3) 2 2 using transformations.Ch. 3.CT - In Problems 4 and 5, a. Determine whether the...Ch. 3.CT - In Problems 4 and 5, a. Determine whether the...Ch. 3.CT - Determine the quadratic function for the given...Ch. 3.CT - Determine whether f( x )=-2 x 2 +12x+3 has a...Ch. 3.CT - Solve, x 2 10x+240 .Ch. 3.CT - The weekly rental cost of a 20-foot recreational...Ch. 3.CT - The price p (in dollars) and the quantity x sold...Ch. 3.CT - Consider these two data sets: One data set follows...Ch. 3.CR - Find the distance between the points P=( 1,3 ) and...Ch. 3.CR - Which of the following points are on the graph of,...Ch. 3.CR - Solve the inequality 5x+30 and graph the solution...Ch. 3.CR - Find the equation of the line containing the...Ch. 3.CR - Find the equation of the line perpendicular to the...Ch. 3.CR - Graph the equation x 2 + y 2 4x+8y5=0 .Ch. 3.CR - Does the following relation represent a function?...Ch. 3.CR - For the function f defined by f( x )= x 2 4x+1 ,...Ch. 3.CR - Find the domain of h(z)= 3z1 6z7 .Ch. 3.CR - Is the following graph the graph of a function?Ch. 3.CR - Consider the function f(x)= x x+4 . a. Is the...Ch. 3.CR - Is the function f(x)= x 2 2x+1 even, odd, or...Ch. 3.CR - Approximate the local maximum values and local...Ch. 3.CR - If f(x)=3x+5 and g(x)=2x+1 , a. Solve f(x)=g( x )...Ch. 3.CR - For the graph of the function f , a. Find the...
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- (14 points) Let S = {(x, y, z) | z = e−(x²+y²), x² + y² ≤ 1}. The surface is the graph of ze(+2) sitting over the unit disk. = (a) (4 points) What is the boundary OS? Explain briefly. (b) (4 points) Let F(x, y, z) = (e³+2 - 2y, xe³±² + y, e²+y). Calculate the curl V × F.arrow_forward(6 points) Let S be the surface z = 1 − x² - y², x² + y² ≤1. The boundary OS of S is the unit circle x² + y² = 1. Let F(x, y, z) = (x², y², z²). Use the Stokes' Theorem to calculate the line integral Hint: First calculate V x F. Jos F F.ds.arrow_forward(28 points) Define T: [0,1] × [−,0] → R3 by T(y, 0) = (cos 0, y, sin 0). Let S be the half-cylinder surface traced out by T. (a) (4 points) Calculate the normal field for S determined by T.arrow_forward
- I need the last answer t=? I did got the answer for the first two this is just homework.arrow_forward7) 8) Let R be the region bounded by the given curves as shown in the figure. If the line x = k divides R into two regions of equal area, find the value of k 7. y = 3√x, y = √x and x = 4 8. y = -2, y = 3, x = −3, and x = −1 -1 2 +1 R Rarrow_forwardSolve this question and show steps.arrow_forward
- u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.arrow_forwardQuestion 3 (6 points) u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (u + v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅ w) Support your answer mathematically or a with a written explanation. d) If possible, find u (v × w) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.arrow_forwardK Find all values x = a where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist. x-7 p(x) = X-7 Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. (Use a comma to separate answers as needed.) OA. f is discontinuous at the single value x = OB. f is discontinuous at the single value x= OC. f is discontinuous at the two values x = OD. f is discontinuous at the two values x = The limit is The limit does not exist and is not co or - ∞. The limit for the smaller value is The limit for the larger value is The limit for the smaller value is The limit for the larger value does not exist and is not c∞ or -arrow_forward
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