Current Attempt in Progress Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. 6xy dx + 4xy dy, where Cis the rectangle bounded by x = - 1, x = 2, y = 2, and y = 6. %3D C. 6xy dx + 4xy dy = i

Q: 1 The partial derivative of f(x, y, z) = Arctan with respect to z is xy? z³

A:

Q: sin 201/1+ 2 sin 0/cos? 0 (sec² 0 – 1) d0 1. |

A: To find the following antiderivative.∫sin 2θ1+2 sin θcos2 θ sec2 θ-1 dθ

Q: (2n)! for 1· 3·5 ... (2n – 1).) 2"n! Use the binomial series to find the Maclaurin series for the…

A:

Q: dw dw Find ду at the point (w, x, y, z) = (75, – 1,2, – 3) if w = 3xy + 3yz- 3z° and x2 +y? +z? =…

A:

Q: Y – C(Y)-I(i)–G, =0 kY +L(i)– M20 =0 %3D

A: answer is in next step

Q: The derivative with respect to x of | (3Vi-1) dr is 3x – 1 by the 2nd fundamental theorem of…

A: Given that,         ∫3x3t-1dt

Q: Find y': y = ar csc(2a2)

A:

Q: 1. Use the right hand rule to determine which of the following vectors ( î, -î, ĵ, -ĵ, k, –k ) would…

A: According to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: Evaluate the double integral.

A:

Q: Evaluate the integral. V3/2 dr V1- r2 |

A: We know, ∫dx1-x2=sin-1(x)

Q: Ir(t) - u(t)] and Ir(t) x u(t)] in two different ways. dt r(t) = cos ti + sin tj + tk, u(t) = j + tk…

A:

Q: Determine whether the infinite geometric series is convergent or divergent. If it is convergent,…

A:

Q: Find the average value of the function f) = 8-7 on the interval [0, 9]. %3D

A:

Q: Q3) Apply the logarithmic differentiation to find the derivatives of: x+1 y=(sinx-x)**

A:

Q: 12 and sin 0 < 0, find (Please show the solution.) 5 If tan 0 = %3D - (a) sin 20 (b) cos 20 (c) tan…

A:

Q: (x^2+y^2-3)dx-2xydy=0 Prove the given DE is exact, and find general solution

A:

Q: Consider f(x) = (5x + 11)2022, find: i. f'(x) ii. f"(x) iii. f''(x) iv. fiv (x) v. f°(x)

A: Given, f(x)=5x+112022

Q: Calculus Use newtons method with the specified initial approximation x1 to find x3 the third…

A: Given

Q: The acceleration function (in m/s2) and the initial velocity v(0) (in m/s) are given for a particle…

A:

Q: arcsin = ab? x? - Va2- y2: Find y'. 2abe (+0) /a-y 1-y 2ab a 1-y 2ab a /a-y %3D

A: We neee to find derivative of y for the function given below:

Q: メーャゴ+2x)dメ+でyalyo

A: answer is in next step .please give a like

Q: For the rational function f(x) = find the following limits and identify the type of asymptote that…

A: Given: Rational function: f(x)=4x-1x+9

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 4 cos(t)i+5 sin(t)j+ 6tk;…

A:

Q: The graph of the function f(x) = sin(x+ 8) is shown along with the points (– 8, f( – 8)) and (– 7,…

A: (1) f(x)=sin(x+8)f'(x)=cos(x+8)slope =f'(-8)=cos(0)=1equation of tangent at…

Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

A:

Q: Evaluate the integral / (4x + 18y) dx + (27x – y)dy along the parabolic arc y = x? from (0,0) to (1,…

A:

Q: EXAMPLE 3 Evaluate the following integral. VI- 4.r2 SOLUTION Let u = 1 - 4x². Then du %3D , SO xdx =…

A: We can solve as follows

Q: Question 2 Determine the derivative of sec(x) tan(x) O sec z + sec z tan? x 2 sec? z tan x sec x O…

A:

Q: an +1 an +1 an + 1 Recall the Ratio Test which states that, if is a series with nonzero terms, and…

A:

Q: If f(x) = [ V19+ t² dt , find f'(3)

A:

Q: A point Q moves along the intersection of the sphere a? + y? + 2² = 1 with the 2. At what rate is z…

A:

Q: Let e, = ( ) be a unit radial vector, where r = Vx? + y + z?. = (1 (a) Calculate the integral of F =…

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin(In 12x) dx Cos In x +…

A:

Q: 6. (ax3+ bx2+cx) dx= 2b | x2dx where a,b and c are constants. -9 A) True B False

A:

Q: Find the general solution of the equation. Express the solution explicitly as a function of the…

A:

Q: Solve the higher order initial-value problem f''(x) = x-1/x + 3 ; f'(1) = 3, f(1) = 0

A:

Q: Solve the initial value problem. 4 y(x) = 4 sec(3.xr) tan(3x) ; y(7) = 3

A:

Q: Find the derivative of the function f(x) = 9r( – 5x + 6z). %3D f'(x) =

A:

Q: (- 1)"(x + 1)" n! Consider the series E n=0 (a) Find the series' radius and interval of convergence.…

A: We will use Ratio Test for convergence

Q: Find the indefinite integral. (Use C for the constant of integration.) 4 dx V 81 – (x + 9)2

A:

Q: / (3V-1)dt is 3- 1 by the 2nd fundamental theorem of Calculus. The derivative with respect to x of 3…

A:

Q: PART III: APPLICATION 5. a and b have magnitudes of 5 and 6, respectively. The angle between them is…

A:

Q: Evaluate. 1 6 x dx V16 +3x2 0. V19 A) B) 2/19 -8 C) V19 -4 - 2 D) -219 +8

A:

Q: Find dy/dx. x = Vt y = 9-t %3D dy dx

A: The objective of the question is find dy/dx.

Q: 10 8. 10 If f (x) dr= 17 and/ f(x) dx= 12, then f(x) dr=5 A) True Ealce

A:

Q: dy Solve the separable differential equation dt t t?y + y Use the following initial condition: y(0)…

A:

Q: Sketch the region enclosed by y = 4x and y = 7x². Decide whether to inte with respect to x or y.…

A: we have to find the area of the region .

Q: Find curl(7z i+ 8x j + 5y k). curl(7z i+ 8x j+ 5y k) = (i )i + ( i )j +( i )k

A:

Q: Find the work done in pushing a car a distance of 12 m while exerting a constant force of 300 N.

A:

Q: For the series below, (a) find the series' radius and interval of convergence. For what values of x…

A: