(a) 8) Show that F = (y? - 4r, 2ry - sin(y)) is conservative. (b) Find a potential for F from part (a). 3) Use the Fundamental Theorem of Line Integrals to evaluate F. dr where F C is the same as in (a) and C is the curve given by x(t) = ; (1 – t) e* –1 v(t) = (t – 1) -1

(a) 8) Show that F = (y? - 4r, 2ry - sin(y)) is conservative. (b) Find a potential for F from part (a). 3) Use the Fundamental Theorem of Line Integrals to evaluate F. dr where F C is the same as in (a) and C is the curve given by x(t) = ; (1 – t) e* –1 v(t) = (t – 1) -1

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.CR: Chapter 6 Review

Problem 35CR

See similar textbooks

Related questions

Q: 8. A solid lies in the 1st octant bounded by the surface y = 9 - x2 (where x 2 0) and the planes y =…

Q: sinc(2nBt – mn) sinc(2nBt n7

Q: dY 6. dt 2 -1 Y 4

Q: (c) The solution of the following problem for the wave equation on the half-line: Utt = Ugr, x > 0,…

Q: 2a +b-c+d = 1 За - 2b + 2с-3d %3D2 2a - b+c- 3d = 4 5а +b-с+ 2d %3D-1

Q: Show that the differential equation UTM dy -2 - ye rey - 2y dr is exact and find its solution.

A: Use the concept of exact differential equations.

Q: Let [g] be an element of order 180 in Z181 Explain the operation of the ElGamal public-key…

A: We will use the basic knowledge of number theory and cryptography to answer this question completely…

Q: 6. Engineers Required 20 55 47 38 90 63 NPV ($1,000,000s) 1.0 1.8 2.0 1.5 3.6 2.2 Formulate an…

A: When project 4 is done, at least two of the other projects will be done. P1+P2+P3>=2P4.

Q: Let A, B be 2 x 2 matrices, C a 3 x 3 matrix and D a 1 × 1 matrix. Find the condition on these…

Q: dx : 2x-y dt %3D dy 3x - 2y + 8t %3D dt

Q: Use the substitution 2 = ry, where z is a function of x, to solve the following differential…

Q: 2. (a) Find the exact length of the curve (i) r = 1+sin 0, 0<0< 27, (ii) r = 2(1+ sin 0), 0 <0< 27.…

Q: Using only the Laplace transform table to obtain the Laplace transform of the following functions:…

Q: Problem 2. (i) Consider the normalized vector v in R3 and the permutation matrix P, respectively 1 v…

Q: 1. Write the first five terms of the sequence defined by each equation. t = 4n b. t=3n-7 а. c. t=(n+…

A: Substitute the first five natural numbers for n in the given sequences to obtain the first five…

Q: +3x f(x) =e

Q: Use variation of parameters to solve the given nonhomogeneous system. X' X(t) =

Q: The amount of coffee in a can has a mean of 350 g and a standard deviation of 4 g. 9) Sketch a…

Q: 7. y=8x* – 12x – 30 x2 – 17x – 3 8. y=x* + 6x³ + 11x² + 6x

Q: а (e) Let B = be any 2 x 2 matrix. COS a [sin a (i) Show that there are real numbers U11 and a such…

A: This is a multipart question having two or more interrelated subparts. As per company policy, we can…

Q: 1. Each set S is linearly independent. Use the Gram-Schmidt process to create an orthogonal set of…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: let fo) - X In (x) , using the following approximation formula for the secowd denvative 1. assuming…

Q: The differential equation (-xysin x+2ycos xdx +2xcos x dy 0 is

Q: Differentiate. f(x) = ex+3x f'(x)=]

Q: O File | file:///C:/Users/tphok/Downloads/Document%20-%202022-05-08T180434.430.pdf Q Update ocument-…

Q: b. Find a rectangular-coordinate equation by eliminating the parameter t.

Q: Find odd and even function (half range) Fourier series of function below f(x) = { 2-x 0 < x< 1 1< x…

Q: a+ 2b+3c-2d =6 3a + 2b -c+2d = 4 2a -b-2c-3d = 2 2a - 3b +2c+d =8

Q: 26 8. Find the indicated term of each harmonic sequence. 1 1 1 1 a. 5'8' 11' 14' 10th term .... 1 1…

Q: 1. Points A(2,1,0), B (4,1,6), C(5,3,s) and E (-8,5,t) are the vertices of a triangular prism where…

Q: From a total of six men and four ladies a committee of three is to be formed. If Mrs. X is not…

A: Solution

Q: determine whether multiplication by A is one-to- one by computing the nullity of A and then applying…

A: Let (x, y) be in nullspace of A. Then, A(x, y)t = 1-22-4-36xy = 000 => x - 2y = 0…

Q: 5. A graph G has 105 vertices of which there are 13 vertices of degree 3, 33 vertices of degree 5…

Q: [4 10 In the matrix A = |2 2 -4 -1, suppose an is the pivot. This means that Row ? ♥ is being zeroed…

A: Given that A=410-525-12-47 To pivot the element a11, find matrix M such that M.A=Pivot matrix

Q: The function 1. f(z, y) 4+4x + 4y can be expressed as a Taylor Series about a 4. y =5 ie. f(z, y) R…

Q: (b) In the interval [-1, 1], the function -x, -1 < x <0 f (x) = x, 0 < x <1 can be represented by a:…

Q: Solve the equation: u = a uxx u(x, 0) = f(x), u(0, t) = ü(L, t) = 0 0 0 %3D

A: We have to find the general solution of given heat equation.

Q: Find D,y using the rules for finding derivatives. y= (sx² -2) (4x- 3x +8) Day= !!

Q: A test program for grade 10 can generate quadratic functions in a standard form y = ax + bx + e…

A: Given quadratic function in a standard form is y=ax2+bx+c wherein coefficients a, b and c are…

Q: 2. Let R = {(x, y) : x,y E R}. Prove or disprove that R is reflexive, symmetric and/or transitive if…

Q: 3. Determine f(x) is e(g(x)) for each of these function f(x) and show a pair of witness C, C2, k and…

A: We will use the basic knowledge of functions to answer this question properly and correctly. Note…

Q: 1) Consider the spiral r:-7, 7 R' defined by (cos(s) r(s) sin(s). i) Compute the unit tangent vector…

A: Please note that clearly, solving part (iv) requires us to solve parts (i), (ii), and (iii). Now,…

Q: 38. Let 2 = R0, the space of all sequences of the form w = (x1, x2, ...) (**) %3! where x; e R. Let…

Q: Use the power series 1 2(-1)" x" to determine a power series, centered at 0, for the function. 1+x…

Q: The following f (t) is a periodic function of period T = 2n, defined over the period –T<t< n. S -2t…

A: We have to express the given function f(t) as a Fourier series expansion.

Q: Is it possible for a basis transition matrix to equal the identity matrix? Explain with an example.

Q: 2. Consider the system dx = -2x + y dt dy = -2y dt and its corresponding direction field. (a) Sketch…

A: First, knowing direction fields and what they tell us about a differential equation and its solution…

Q: B. Evaluate the double integral Se S f(r,0) dA, and sketch the region R. -n ccos e r dr de

A: Here to sketch the region using polar coordinates x=rcos(theta) y=rsin(theta) then we get the curve…

Q: Given the vector field F⃗ = (z, x, y), calculate the flux of the curl of F⃗ through the portion of…

A: Stokes theorem: flux of curl of a vector field us equal to the line integral of the vector field…

Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for…

Question

All part's please in 30 minutes and get the thumbs up please show neat and clean work

(a)
8) Show that F = (y? - 4r, 2ry - sin(y)) is conservative.
(b)
Find a potential for F from part (a).
3) Use the Fundamental Theorem of Line Integrals to evaluate
F. dr where F
C
is the same as in (a) and C is the curve given by
z(t) = 5 (1 – t) e"-1
v(t) = 7 (t – 1)
¤(t)
-1<t<1,
%3D
%3D

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Let f be the function defined by f(x) = √3x^2 + 2a) Find the differential of f.b) Find the approximate change in y = f(x) if x changes from 4 to 4.1
Q.3) (a) Evalute |(22 – y?)dx + 2ydy, along the circular arc C that is upper half circle oriented counterclock wise. (b) Can you apply the Green's theoren to evalute the line integral in the above question. Explain your ideas.
Suppose F(x, y) = −y sin(x)i + cos(x)}. (a) Find a vector parametric equation for the parabola y = x² from the origin to the point (2, 4) using t as a parameter. r(t) = (b) Find the line integral of along the parabola y = x² from the origin to (2, 4).
Let f(x, y) = sin(15x2 + 3y2) Calculate the quadratic approximation of f at the point (0,0)
3. Let f(x, y) = 14-x² - y² and P = (1, 2). Find the directional derivative of f at P in the direction of the point Q = (3, 4).
B. Find the derivative of function f(x, y, z) = 3e* cosxy + ez + Inzx at point P(1,0,) in the direction = 1 + 2] + 2k JAF 3
Evaluate the line integral (8x + 7y)dx + (2x - 7y)dy along the | curve C: r = 8 cos t, y = 16 sin t (0 < ts-) T NOTE: Enter the exact answer. | (8x + 7y)dx + (2x – 7y)dy =
4. Let f (x) = x³ -x² + 5. a) Find the y-intercept of f. y-intercept: b) Find f' and f", and determine where each are 0 and/or do not exist (DNE). If none, write "none". f' = 0: f' DNE: f" = 0: f" DNE: c) E Do a sign analysis on f' and f". d) Find the intervals on which f is increasing and decreasing. Increasing: Decreasing: e) Find the intervals on which f is concave up and concave down. Concave up: Concave down: f) answers as (x, y) points. Find all local maxima, local minima, and inflection points of f. Be sure to write your Local max: Local min: Inflection point(s): -4 -3 -1 g) Sketch the graph of f.
Let f(t) be the velocity in meters/second of a car at time t in seconds. Give an integral for the change of position of the car. (a) For the time interval 0