Find the general solution 2x'y - (2x + y) = 0

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

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Q: Evaluate the surface integral. /| xz ds, S is the part of the plane 2x + 2y + z= 4 that lies in the…

A: We need to find surface integral.

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = – 2tj %3D

A: 1st derivative, 2nd derivative, dot product and cross product are evaluated.

Q: Set up a double integral to find the volume of the solid region bounded by the graphs of the…

A: Given problem:-

Q: Find the absolute maximum and minimum values of f(x, y) = (x^2)y of the set D = {(x, y): x ≥ 0, y ≥…

A: To find the maxima and minima first diffrenciate and then equate it to zero.

Q: 4. Let em² cos , 2.x + b, r 0 r>0 h(x) = %3D where b is a constant. (a) Explain why h(x) is…

A: We need to solve continuity problem.

Q: D) 2/0- D)-2y/C 9) Given a piecewise function below f(x) = (1- x)*n (x>0) , Find lim f(x) =r hpli te…

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Q: Solve the differential equation Bernoulli Equations: (x² + y²)dx – xydy = 0

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Q: -Find Taylor or Maclaurin for the following functions: 1) f(x) = sin 3x

A: In this question we can find the Maclaurin series for the function. Maclaurin series for the…

Q: 1 Evaluate dx. - 2x 10 + e 1 dx 2x + C 10 + e

A: To solve the following integral problem

Q: Line segment AB is a diameter of the x² +y² + z² - 2z + 8y = 9. Find point B if A = (0, у, 0).

A: To find the point B if Coordinates  of A are given for the sphere.

Q: Solve the differential equation Integrating Factor by Linear Equation: y' = 1 – 2ycot2x

A: We can solve this as follows:

Q: Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 <ts 1. / (x+ 3y²) dy #4

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Q: Describe the graph of the equation. r = - 2i + tj + (t² – 1)k O Itis a parabola in the x = 2 plane,…

A: Here we  have to identify the vector.

Q: ||r(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = 11 cos(8t)i+11 sin(8t)j+ 3tk…

A: r(t)=11cos(8t)i+11sin(8t)j+3tkr'(t)=d11cos(8t)dti+d11sin(8t)dtj+d3tdtk=-88sin(8t)i+88cos(8t)j+3kr''(…

Q: Find the critical points of the parametric equations x = 5 – Int y = t+ Int

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Q: 5. lim x-0 e2x-1

A: LetL=limx→ 0xe2x-1Plug in the value x=0L=0e2(0)-1L=01-1L=00Therefore Apply L Hospital ruleL=limx→…

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 8 1 lim t→+∞\ 5t2 +6' 8t (?, ?)

A: To evaluate the following limit.limt→+∞t2+85t2+6, 18t=?, ?

Q: 22. (x+1)v2r-1 dr

A: Note: According to our expert guidelines only one individual question is to be answered kindly…

Q: dy 4 + 4y = xe'

A: To solve the differential equation by using method of undetermined coefficients.

Q: 2. lim

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Q: A line, passing through point (6, 3, 2) and is perpendicular to the xy-plane. Find a point on this…

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Q: ||r(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find «(t). 13 r(t) = t'i+ t®j 30 t3 K(t) V4 + 25…

A:

Q: 2.) Sž sin"(x)dx

A: sin2x +cos2x =1 dcos xdx=-sin x ∫un du = un+1n+1+C

Q: ててーXつ (ーフ 1 प. ८ genc 16)Find the power Series S こひ( れこス て24(O t2u(コ

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Q: )Solve for k such that 1 k(x2 – 2x + 1)dx = 5 - 0.

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Q: INTRODUCTION TO MATRICES Answer the following questions: Given the Matrix A below. 3 12 21 A- 17 15…

A: This is a problem related to matrix . Based on the general formula and concepts we will answer the…

Q: 4 4 4 + + 9. 27 3 +

A: Given problem:- (4/3) +(4/9) +(4/27) + ........  Determine whether given  geometric series…

Q: The integral TT tan x sec?x dx is an improper integral of type I that diverges is an improper…

A: To evaluate the following integral.∫π2π tan x sec2 x dx

Q: Evaluate the double integral. 5x (4 + y)¯² dA; R R is the region in the first quadrant enclosed by y…

A:

Q: Find curl (4zi+ 5xj+8yk). curl(4zi+ 5xj+ 8y k) = ( i )i + ( i )j+( i %3D

A: As we know that; The expression for the curl of the vector point function F→=F1i+F2j+F3k is; curl…

Q: 6. lim (sinx)*

A:

Q: 2. SET-UP the definite integral that will give the area of the region specified using (a) x as the…

A: Area

Q: Set up a triple integral for the volume of the solid. Do not evaluate the integral. The solid in the…

A: Volume

Q: 2) (-2)77"= 5h hzo

A:

Q: A local pond can only hold up to 51 geese. Seven geese are introduced into the pond. Assume that the…

A: This is a problem related to differential equation and exponential function. Based on the general…

Q: ||r(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = ti + t°j

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Q: given poim arctan(2) f(x, y) = arctan (4, -4) f(X, y) = x, ) = (4, -4) = (4,-4) =

A:

Q: ind the volume of the shaded region when revolved about the indicated axis. 21 * = V7+y 14

A:

Q: Find the volume of the solid generated when the region enclosed by the given curves is revolved…

A: Plotting given curves on the graph

Q: -2x (1+ee) dx e

A:

Q: d Caleulate fri(t) - r(t)] and ri(e) x ra(t)] first by differentiating the product directly and then…

A:

Q: ) Sypposef and g are functionns with continu lerivatives, and that they satisty the followia…

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

Q: Q4: Find the corresponding Spherical polar coordinates of the Cartesian coordinates (6,2,5).

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Q: ピ+5 1 lim t+oo 5t2+6' 8t

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Q: n" is convergent. (2n)! Show that the series > n=1

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Q: Question 1 Find the centroid of the given region. y-2- A (8/23,76/111) B (5,15) (c (3/22,45/61)…

A: The expression for the centroid is: For the x coordinate of the centroid: x=1A∬xdydx  For the y…

Q: Find div F and curl F if F(x, y, z) = 17y®z*i – 8x'z®j – 4cy°k. %3D - div F= curl F=

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Q: L. dr 16. (I + 2)² 1 dz 17. x(x+2) 18. / arctan Vr dr

A:

Q: Find div F and curl F if F(x, y, z) = 14y°z°i – 10x°z°j – 5xy°k. 35: 6.8 - div F= curl F=

A: We have to find div F and curl F.