Find the distance between the skew lines defined by L1: ri(t) =< 1 +t,2 + 6t, 2t > L2:r5 (s) =< 2+ 2s, 4 + 14s, 5s >

Q: Evaluate the line integral ſc 2y dx + 6x dy where C is the straight line path from (4, 1) to (6, 5).…

A: Given query is to find the integral.

Q: Let y = 3x + 2x + 4. If Ax = 0.4 at x = 1, use linear approximation to estimate Ay Ay =

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Q: Let y = 2x + 7x +3. If Ax = 0.3 at x = 4, use linear approximation to estimate Ay Ay 2

A: Linear approximation

Q: 2. Evaluate the given line integral, | (-y,x – y) · dR, where C is the line segment from (1,0) to…

A: To find the line integral we use the equation of line segment in parametric form using given points.

Q: 2. Evaluate the given line integral, (-y,x – y) · dR, where C is the line segment from (1, 0) to…

A: Introduction: The formula of line integral of the function f(x,y) on the line segment C(t) is given…

Q: Rotate the region bounded by y = 6e 2" and y = 6+ 4x - 2x between a = 0 and a = 1 about the line y =…

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Q: s) find the general sduton of second dilferential equation 3y"+2y'+y=0

A: Consider the given differential equation 3y" + 2y' + y = 0

Q: Let y = 2x2 + 7x +3. If Aæ 0.3 at r 4, use linear approximation to estimate Ay %3D Ay 2 instructor

A: Linear approximation

Q: The value of the line integral S(2xy dx + 2x?ydy + dz) C along a path joining the origin and the…

A: We have to find the value of given line integral.

Q: Find the location and velocity at t = 4 of a particle whose path satisfies dt dr (3t-1/2, 5, 8t) and…

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Q: Given etye -Z+ xy - e-0, use e =0, use impicit partial denvatve to finid 2ž at the Point (1 2t

A: Explanation of the solution is given below....

Q: The area bounded by the curve y3a and the lines z 4 and a-9 above the z-azis is aquare units O 27v0…

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Q: Let y = 5x² + 8x + 4. If Ax = 0.4 at x = 2, use linear approximation to estimate Ay Ay a

A: By linear approximation we can write,       ∆y ≈ dy = f'(x) dx Also We have,          ∆y =…

Q: of the valve matix is consistant e an linear

A: Given augmented matrix is: -412h2-6-3 Let the variables be x, y. The above augmented matrix will…

Q: Evaluate f S S 4.x² + 4y² + 4z² dV, where R is the hemisphere centered at the origin, R having…

A: Given that:- ∫∫∫R 4x2+4y2+4z2 dv where R is thehemisphere centered at the origine havingradius 2.…

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

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Q: Let y = 3x + 3x + 2. If Aa = 0.4 at x = 1, use linear approximation to estimate Ay | Ay a

A: We have to find the change in y using linear approximation

Q: Let y = sin(2a). If Ax 0.1 at x = 0, use linear approximation to estimate Ay %3D Ay 2 = Find the…

A: In this question, concept of Linear Approximation is used. Linear Approximation The equation of a…

Q: A cylinder of radius r and height h has volume V = nr 2h.(a) Use the Linear Approximation to show…

A: Given: A cylinder of radius r and height h has volume V=πr2h a)  show:  ΔVV≈2Δrr+Δhhb)  Percentage…

Q: Figure Q2 shows an 11 m long steel beam AC of uniform cross-section, simply supported at left end A…

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Q: Evaluate the line integral fe y dx + x dy where C is the parameterized path x = , y = f, 3 <iS9.…

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Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation to the indicated value.…

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Q: Let y = 2x + 5x +. 2. If Ax = 0.4 at a = 4, use linear approximation to estimate Ay Ay =

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Q: Let y = sin(5x). If Aa 0.1 at z = 0, use linear approximation to estimate Ay Ay 2 Find the…

A: solution

Q: W= Pcxiy,Z) = In (x+y+z) ,x= cost, 2. %3D 2X = Cost, y- Sint and z= 4VE >use chain rule to Rind dw…

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Q: The line integral 2xe" dæ + a²e" dy + (1 – 2²)e¬²² dz is not independent of path.

A: The line integral ∫CF·dr is independent of path if the curl of F is zero, that is, ∇×F=0. Here, The…

Q: Let y = 4x2 + 7x + 4. If Az = 0.2 at z 4, use linear approximation to estimate Ay Ay s

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Q: Evaluate x*dx C + xy dy, where C is the triangular curve consisting of the line segments from (0, 0)…

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Q: Let y = 5x + 2x +3. If Ax = 0.1 at x = 3, use linear approximation to estimate Ay %3D Ay 2 Ouestion…

A: We have to find

Q: 2. Evaluate the given line integral, (-y,x – y) · dR, where C is the line segment from (1,0) to…

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Q: Compute 6xy da dy, where D is bounded by the curves y = 4 – x2 and y = 2x + 4.

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Q: Let y = 5x + 4c +3. If Ar 0.1 at z 5, use linear approximation to estimate Ay

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Q: Let y = sin(4x). If Ax 0.4 at z 0, use linear approximation to estimate Ay Ay 2 - Find the…

A: Solution :-

Q: Let y 522 + 2x + 3. If Aæ = 0.4 at x = 3, use linear approximation to estimate Ay Ay =

A:

Q: Let y = sin(5x). If Ar = 0.4 at r = 0, use linear approximation to estimate Ay Ay 2 %3D Find the…

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Q: 4. (a) Use the trapezoidal rule to numerically integrate from a = 0 to b= 2 /(z)-0.2+25 +3r

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Q: Let y = 4x + 2x + 4. If Ax = 0.1 at x = 2, use linear approximation to estimate Ay %3D %3D Ay 2

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Q: Find the line integral (4х — 5у) ds, where C is the semicircle y = 9 – x² traversed from (3,0) to…

A: Graph the semi-circle. Take x=3cost and y=3sint Now, x'=-3sint and y'=3cost The angle covered by…

Q: Let y 5x? + 4x + 3. If Ar 0.1 at I = 5, use linear approximation to estimate Ay

A:

Q: The value of the line integral S(2xy²dx + 2a?ydy + dz) along a path joining the origin and the point…

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Q: 2x dV, where E is bounded by the paraboloid x = 2y2 + 2z2 and the plane x = 2. %3D

A: The given integral is ∭E2xdV. The region E is bounded by the paraboloid x=2y2+2z2 and the plane x=2.…

Q: Show that the line integral / 2re" dx + (2y – x²e¯") dy is independent of path where C is any path -…

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Q: Employ the classical fourth-order Runge-Kutta (RK) method to integrate dy = y – t² + 1 dt

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Q: Let y = 3x +7x+ 4. If Ax = 0.4 at a = 1, use linear approximation to estimate Ay %3D Ay 2

A:

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

A: Consider the given function, Tx,y=100-x2-2y2 the differentiate partially, ∇T=-2x, -4y the slope at…

Q: 4x Estimate the error in the quadratic approximation of f(x,y) = e sin y at the origin over the…

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Q: Let y sin(5x). If Ar 0.3 at z 0, use linear approximation to estimate Ay %3D Ay = = Find the…

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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