Evaluate yz dx +y dy +a dz, where C is the line segment from (2,0, –1) to (4, 1, 2).

Q: %3D %3D dz Find at (2, -2, 1) if x + y? +z2 = 6xz+6yz+21 = 5 =D1

A: Given equation : x2+y2+z2=6xz+6yz+21

Q: y"(t) – 4y'(t) + 5y(t) = e"U (t – 2), %3D

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Q: 2. Let j = Find the point on the line y x that is closest to j. %3D %3D 26

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Q: 2. Evaluate f. (y²dx + x?dy) where C is the triangle with vertices (1, 0), (1, 1), (0, 0).

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Q: Where f(x, y) y calculate (–1, 1) towards the point dv (-1, 3)

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Q: Compute Ay and dy for the given values of x and dx = Ax. y = x2 - 7x, x= 6, Ax = 0.5 %3D %3D dy =…

A: Given y=x2-7x, x=6, dx=∆x ⇒dy=dydx·dx and ∆y=y(x+∆x)-y(x)

Q: f(x, y, z) = ln(x² + y² + z²) at the point P(1, 3, 2) in the direction of

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Q: We know that Sclf(x,y)dx +g(x, y)dy] = Sf(x, y)dx + S, g(x,y)dy. Use Sef(x,y)dx + S g(x, y)dy. Use…

A: We need to evaluate the integral ∫Cydx+xdy where C is the line segment from (1,-1) to (4,3).

Q: Find (x2 + y)i + 3y j) · dř where C consists of the three line segments from (5, 0, 0) to (5, 4, 0)…

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Q: E valuate / (x² + iy³) dz, where C is the straight line from z = 1 to z = i. %3D

A: We have to evaluate ∫Cx2+iy3dz, where C is the straight line from z=1 to z=i. Since we have z=x+iy…

Q: Evaluate [(-x+y + 2)dx + (x+y-2)dy + (x-y+z) dz where C is the line segment from (-1, 2, 3) to…

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Q: dw dw Find ду at the point (w, x, y, z) = (- 4,1, - 1,1) if w = 4x y + 4yz - 4z° and x? + y? + z² =…

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Q: II. Find the acute angle between the given curves. 1. y'=2x^4x+4y'+5 y=0 2. x'y+4a y=8a°nx²=4 ay 3.…

A: As per bartleby guidelines we only give first question answers.

Q: Using the substitutions X = u+2, y=w+2; dx = du, dy= dw, the DE with linear coefficients (x + y-…

A: Using the substitutions X=u+2, y=w+2; dx = du, dy=dw, the DE with linear coefficients (x+y-4) dx +…

Q: Find a point on the curve y = x² that is closest to the point (18, 0). %3D AY y =2 (x, y) (18, 0)

A: Find a point on the curve y=x2 that is closest to the point  Here use distance formula…

Q: Express the curve by an equation in x and y given x(t) = e' and y(t) = 7 – e2'. a) O-x2 + y = 7, x 2…

A: simplify the equation and choose correct equation.

Q: At the given point, find the line that is normal to the curve. 2x y-cos y 3x, (1,x) 1 O A. y= -7**7…

A: The given curve is 2x2y – π cosy = 3π and the point is (1, π). Evaluate the slope of the tangent to…

Q: (d) The curve y = x – x² from r = 0 to r = 2

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Q: Evaluate . y? cos(x) dx + 2ysin(x)dy where C is the straight line between (0,0) and

A: The equations of the straight line joining (0,0)to π2,1 are x-0π/2-0=y-01-0=t(say) i.e. xπ/2=y1=t…

Q: Compute Ay and dy for the given values of x and dx = Ax. у- х2 - 4х, х - з, дх - 0.5 Ay = dy Sketch…

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Q: v(e -Y cos x) • dr, where C is the line from (0,0) to (2x, kn 7)

A: The fundamental theorem of line integral, also known as gradient theorem states that suppose a curve…

Q: (A) Evaluate" [(x² + y)dx + (x+1+d along the path ABCA shown in figure C(0,3) A(0,1) x=3sint y=3cost…

A: What is Line Integral: When we integrate a function along a straight line or a curve inspite of…

Q: Find Dy, Dx and the value of x, y,z    x + y + z = 2   6x -4y+5z=31   5x +2y+2z=13

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Q: Find the orthogonal trajectory to the family of curves: y(x²+1) = Cx

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Q: .2 y = x", y = 2x, about the line x = 0 using the method of disks or washers. 4 Volume…

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Q: ) Find the gavea d the rgion enclased by the line x-In3 and the curves y= ex and y=ex

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Q: fc z2 dx+ x2 dy +y2 dz, C is the line segment from (1,0,0) to  (4,1,2)

A: Given, r(t)=z2dx+x2dy+y2dz We have the line segment from (1,0,0) to (4,1,2) We parametrize the given…

Q: Evaluate S(-x+y+z) dx + (x+y-3) dy + (x-y+z) dz where C is the line segment from (-1, 2, 3) to…

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Q: If F(x,y) = 3y. i+5x-j, find SF . •dr where Cis the straight-line path from (0,0) to (1,0), to (0,1)…

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Q: Evaluate xy dx + a*dy, where C is the rectangle with vertices (0,0), (2,0), (2,1), and (0,1)

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Q: Evaluate.(2y dx + 4zdy + 3x dz)where C consists of the line segment C, from (1, 0, 0) to (4, 5, 6),…

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Q: Find Vq if (a) =In (r) %3D (b) p= In (-) %3D We know r= /x² + y² + z2

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Q: Evaluate S(-x+y+z)dx + (x+y-z)dy + (x-y+z) dz where C is the line segment from (-1, 2, 3) to (3,-2,…

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Q: Integrate h (x. y.2) = yzi+xj+xzk over the indicated path: the line segment from (0. 0. 0) to (1. 1,…

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Q: Find the values of dz/ôx and az/ðy at the points 31. z - xy + yz + y -2 = 0, (1, 1, 1)

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Q: ƒ(x, y) = 4x - 8xy + 2y + 1 on the triangular plate bounded by the lines x = 0, y = 0, x + y = 1 in…

A: Given function f(x, y),f(x, y) = 4x-8xy+2y+1             ........................(1)Given conditions…

Q: find dw/dx, dw/dy, dw/dz using implicit differentation. Leave your answer in terms of x,y,z,and w.…

A: To find the implicit differentiation of the function: ln(2x2+y-z5+11w)=z...(1) So, take w as a…

Q: Find the orthogonal trajectory of the curve x^2 + y^2 = 2 ln cx

A: Given query is to find the orthogonal trajectory of the curve.

Q: Find (au/ay) at the point (u,v)=(√6,-2), if x=u² + v² and y = uv. du = (Simplify your answer.) dy)…

A: ANSWER: 1

Q: Find dy/dx. - tsin(t), y = t² + 5t %3D %3D

A: givenx=tsinty=t2+5tfirst we differentiate these two then we evaluate dydtdxdt which is equal to dydx

Q: az Find at (2, -2, 1) if x2 + y? + z2 = 6xz+ 6yz + 21 %3D 8. %3D %3D dy %3D 25 25 1.

A: Given,x2 + y2 + z2 = 6xz + 6yz + 21

Q: If x"y" = (x + y)"** m. m+n Then, P rove that dx?

A: Double derivative

Q: Evaluate I=∫C(sinx+4y)dx+(5x+y)dy for the nonclosed path ABCD. A=(0,0), B=(1,1) ,C=(1,2), D=(0,3)

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Q: Find dy/dx and d62y/dx62 at the given point without eliminating the parameter. x=1/2t^2+9…

A: Given parametric equations are: x = 1/2t2 + 9 y = 1/3t3 + 4t Differentiating x with respect to t we…

Q: Compute ∫C y dx + xy dy if C goes from (0, 0) to (1, 2) along the line parameterized as x = t, y =…

A: Here I am attaching image so that you understand each and every step.

Q: S. 3 z dz where C is straight line segment from i to -2 - 3i

A: We put z=x+iy And dz=dx+idy

Q: dy find 3 - x x - 2 1) If y = t + 2t , t = %3D %3D dx

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

Q: Integrate h (x, y. 2) = yzi+xj+xzk over the indicated path: (a) the line segment from (0, 0. 0) to…

A: definite integrate calculus