Define f (x,y) = 3y √1+x² a. Find the rate of change of f at the point (-1, 1) along the direction <1, -1>. b. Let C be the portion of the curve y = - −x³ from the point (-1, ½) to the point (3, -9). Evaluate ſc f(x,y)ds.

Define f (x,y) = 3y √1+x² a. Find the rate of change of f at the point (-1, 1) along the direction <1, -1>. b. Let C be the portion of the curve y = - −x³ from the point (-1, ½) to the point (3, -9). Evaluate ſc f(x,y)ds.

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.

Chapter7: Integration

Section7.1: Antiderivatives

Problem 45E

See similar textbooks

Related questions

Q: If f(x) = 1 - log5 x, then f-¹(x) =

Q: A smooth curve C is defined by some vector function R(t) with R = (π, 0, -2) and R '(t)= (2, √5 csc…

A: Since you have asked multiple questions, we will solve the Question Q(1) and (2) for you. If you…

Q: 2) Find an equation of the plane that contains all points that are equidistant from the points…

Q: 2b) What are the eigenvalues of (A - σI)-¹? Hint: Your answer should eigenvalues of A−¹ are involve…

Q: 2. integer. Give a recursive algorithm for computing n(n+1), where n is a non-negative

A: We know, sum of first n positive integers = 1 + 2 + 3 + . . . . . . + n = n(n+1)/2 => 2 (…

Q: Do the following for the points (-4,-259), (-1,-4), (3, -84), (4, -259): (If you are entering…

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

Q: Set up an interated triple integral equal to √3 x²+y² I = 1 flaxe 2y dz dy dx -√3- 2-√4-x²y² using…

Q: Prove that using the only the form of the given equation (no graphing) that it is a paraboloid.…

A: We need to prove that the the equation: x2+z2-y4=1 is a paraboloid.

Q: Tom Brady throws a 12 yard out route to Antonio Brown. Even though the pass only gained 12 yards,…

A: Given: Antonio Brown receives a 12-yard pass from Tom Brady. Despite the fact that the pass only…

Q: Use separation of variables to find solution for the given partial d²u differential equation 4- -…

Q: Let R be the region bounded by the graphs of y=x²-3 and x = y². (a) Find the area of R. (Round your…

A: Given that R be the region bounded by the graph of y=x2−3 and x=y2. a We have to find the area of R.…

Q: Bobby's car has a 70-L fuel tank and a fuel efficiency rating of 6.5 L/100 km. How far can he travel…

A: Introduction: In mathematics, unitary method is a basic method. This method is used in many field of…

Q: Use the Adams-Bashforth-Moulton method to approximate y(1.0), where y(x) is the solution of the…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: 4. a) Prove that i) V=I ii) fx+nh = ! I+A 1+A (1) AK fx. = 4k=0

A: Introduction: In numerical analysis, there are many different operators that are used. These…

Q: Solve the PDEs. p2x + q2y = z. Handwriting solution

Q: 15:00 liverpool.mobius.cloud a. Find the Laplace transform of f(t) = t5 e6t (using the tables given…

A: Disclaimer: Since you have asked multiple question, we will solve the first question (part a) for…

Q: Let there are 6 states then how many ways to arnage the trnasition matrix?

A: Introduction: Transition matrix is used in many different fields of mathematics. In Markov chain…

Q: Question 2. Find the general solution of the given ODE for t > 0, t²x" − t(t+2)x' + (t + 2)x = t³e¹.…

Q: . f(x, y) = 1 + y + x cos y at Po(0, 0), R: x ≤ 0.2, y ≤ 0.2 (Use cos y ≤ 1 and sin y ≤ 1 in…

A: Linearization of the function and bound on the error.

Q: Let S be the surfaced defined by the vector function R(u, v) =, u € [0,2], VE [-1, 1]. a. Find an…

A: The equation of the surface given is as follows: R→u, v=eu, ev, u2+v2 Where, u∈0, 2 and v∈-1, 1.…

Q: 2. Suppose you start a business making and selling earrings. Your cost to make each pair of earrings…

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

Q: Determine whether the given matrix A is diagonalizable. If so, find the matrix P that diagonalizes A…

Q: Population growth of any species is frequently modeled by an ODE of the form where N is the…

A: Introduction: Runge-Kutta method of order four is an advanced method that is used to approximate the…

Q: If the radius of the planet Mars is measured to be 3350 km, with a measurement error of plus or…

A: Given information Radius r=3350 km. Error Δr=±100 km. Since, volume of the planet is given by…

Q: Please solve the initial value problem and show your work clearly. Thank you.

A: Introduction: Calculus is a branch of mathematics that focuses on rates of change, differential…

Q: Find and sketch the domain of f(x,y)=√1 - (x + 1)² − y² + 2 ln(x − y + 1) -

A: We need to determine and graph the domain for the function: f(x, y)=1-x+12-y2+2lnx-y+1.

Q: There are 3 types of boilers in a glove company, namely boiler A, B and C. The utility cost per hour…

Q: Find the Fourier series for the following functions: f(t) = |sin t], -1 < t < n

Q: Let x1, x2, x3 be solutions of the following ODE t^x''+2tx''+x'+2022x=0 for t>0 If their Wronskian…

A: Given differential equation is t2x'''+2tx''+x'+2022x=0 and W2=20. We have to find the Wt for all…

Q: Set up an iterated triple integral equal to 3 1 = √√³/0² x²+y² 3 √2-√4x²-² 2y dz dy dx 3-x² using:…

Q: Show that lim (x,y)→(0,0) 16x4+9y12 4x²+3y6 does not exist.

Q: Set up an iterated triple integral equal to | = √√3 √3-x² √√30 x²+y² 3 √2-√4-x²-y² 2y dz dy dx…

A: The given problem is to set the given triple integral in Cartesian coordinates to convert into the…

Q: Solvex (az + √2) dx − y(az + √2) sin (ay²) dy + (az √2) dz = 0

A: Integrate both sides

Q: Consider the following matrix: A = (²³) 3) Problem E.1.d. If the matrix A is diagonalizable, find…

A: We have to solve given problem:

Q: Use the method of undetermined coefficients to find a general solution to the system x'(t) = Ax(t) +…

A: Introduction: one or more derivatives of a function are included in an equation. Equations involving…

Q: Define S to be the following relation on R[x]: S = {(f, g) = R [x]²: (x + 1) divides (g - f) in R[x]…

Q: fine the force field F(x, y, z) = . Find the divergence and curl of F. Let C be the directed line…

Q: Given f(x) = xe¯ = ++ (−1)”x”+1 n! [+0⁰ 'n=0 Solve for the value of f(2022) (0). Solve for the exact…

Q: Find the number of equilibrium solutions of the r x' = x(y-2) โม่ = x − y

A: x'=x(y-2)y'=(x-y) Equilibrium solution of a system of differential equation X'=AX are those solution…

Q: Consider a second order Ordinary Differential Equations (ODES) of the form y" + xy = 0 where y is…

Q: t²x"" +2tx" + x' +2022x 0 for t> 0. If their Wronskian satisfies W(2) = 20, then find W(t) for all t…

Q: (a) If f is continuous and | ₁² f(x) dx = 8, show that f takes on the value 4 at least once on the…

A: We will use the fact ∫abf(x) dx represent area bounded by curve y=f(x) and x-axis from x=a to x=b

Q: An auto repair shop borrowed $12,000 to be repaid by quarterly payments over 4 years. Interest on…

A: given that, P0=12000r=8100=0.08k=4n=4 a. Let R be the periodic payment.…

Q: VII. Suppose is the surface generated by revolving the curve y = 4(²-1) about the y-axis. 1.…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first two sub…

Q: The population of ants in a colony grows at a rate proportional to the number of ants P present at…

Q: Σ 1+4+1 6 is equal to

Q: Rachel purchased a car for $23,900; she paid 20% of the cost as a down payment and financed the…

A: The compound interest formula for an initial amount of P at a rate of r%, for t years compounded n…

Q: Calculate the Fourier series of function f(x)=x^2 -L<x<L using the Fourier series of function…

Q: olve the following linear programming problem using the Simplex method. Where: X1= Amount to invest…

A: We will use slack variable to solve given linear programming in simplex method Note : As 2nd…

Q: X. Let C = C₁ U C2 U C3, where C₁ is the line segment from (-1,-1) to (0,0), C₂ is the line segment…

Question

,, ,,

Define f (x,y)
=
3y
1+x4
a. Find the rate of change of f at the point (-1, 1) along the direction <1, -1>.
b. Let C be the portion of the curve y = -x³ from the point (-1, 3) to the point
(3, -9). Evaluate f f(x,y)ds.

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 5

Step 6

Step by step

Solved in 6 steps with 5 images

SEE SOLUTION Check out a sample Q&A here