Evaluate + 2x + 1)dx+ (2xy+4y- 1)dy along the given path C from (0,0) to (1,1). 5. The straight-line path. 6. The parabolic path y x. %3D

Q: 20) Let y=7x+5x Then compute dy and Ay for X= -7 and dx =0.4. dy =? and Ay = ? Gounded 6o 4 decimal…

A: Derivative: - The derivative of the function is the equation that we find. The instantaneous rate of…

Q: Given y - xy? – x²y=2. Then, at the point (1,2), -is dx

A: let the function is f  first differentiate function f with respect of x df/dx then differentiate…

Q: 2.) Find the acute angle between the given curves y² = 2x and 4x²+ 4y² +5y=0

A:

Q: Which of the following is dy for the curve dx defined by x° – y³ = 2xy? 3x2-2y а. 2x+3y2 3x2-2y b.…

A: Find the derivative of the given curve and match with the correct option.

Q: If w = (y-z)(z-x )(x-y),find the value of dw, dw, dw +- Z-X + dx dy dz

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Q: d. Use your answers for parts a and b to estimate 1 -dx using the trapezoid rule with n=4

A: Approximate by trapezoid rule

Q: Find the coordinates at times t 0, 1, 4 of a particle following the path x -(5+5t').y D 6-8t. t = 0:…

A: To find : co-ordinates at time t,  Just put value of t in equation of x and y.

Q: Find and dm dk at m=k=1 Note: P=x? y + y? z + x² z x=m+k, y= m-k, z= m k (dP/dm)=1 and (dP/dk)=1 O…

A: Given, the function                                 P=x2y+y2z+x2z, where x=m+k, y=m-k, and z=mk then…

Q: | (2x - y) dx + (x + 9y) dy. Ic Evaluate C: x-axis from (0, 0) to (0, -9) and (0, -9) to (5, -9)

A: We can solve as follows

Q: An object is moving along a path defined by the graph  x^2+y^2=18 Compute  dy/dy, if dx/dt=-2,…

A: According to the question:

Q: Which of the following gives the length of the curve y = Vx over the closed interval [1,4]? (A) - dx…

A: Explanation and solutions is given below....

Q: The Bernoulli's Equation dy/dx - y[1/(2x)] - y^5 = O can be transformed in which of the following…

A:

Q: (0) X. 人セこトン (242) 27 vay 4th 15 where Cis the path from P(0,0 to evaluate つlxe し use Green's…

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Q: 1) Evaluate S,(x – y)dx + (y – z)dy + xdz where C is the curve from (1. –2, 3) to (–4, 5, 2) if a) C…

A: Given integral: ∫Cx-ydx+y-zdy+xdz Here, C is the curve from 1,-2,3 to -4,5,2 a) The parametric…

Q: 6. Find dyldx and d 2yldx 2. For which values of t is the curve concave upward? x = t 3 - 48t, y = t…

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Q: Which of the following gives the length of the graph of x = y3 from y = - 2 to y=2? 1+y° dy |1+9y*…

A: sol given   x= y       y = -2 to y = 2   arc length = ∫y =ay= b 1+ (g1 (y)2 dy

Q: 1. Find the length of the curve: y = x/2 , x = 0 to x = 4

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Q: 14. Calculate | (y? – z)dx + (2ry)dy+(2z-x)dz where C is the path along (t2 + 4t + 2, V4+ 5t, t –…

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Q: C is polygonal path from (0, 0) to (3,0) to (3, 2); the sur- face is f(x, y) = 2x +y

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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: Given y - xy? – x²y=2. Then, at the point (1,2), -is dx Blank 1

A:

Q: 2) Determine dz/dx and dz/dy for z* – y? + x² = 6x²y³z? %3D

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Q: La y dx + 2x dy where C is the path along y = Evaluate 2x² from (-1,2) to (2,8).

A:

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

A:

Q: xy*dx + x?dy, where C is the le with vertices (0,0), (4,0), (4,5), and

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Q: Find orthogoral trajectory to the family of dircles 3 x² + y? = 2Cy.

A: We have given equation of curve x2+y2=2Cy Then, differentiate both sides we get…

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: Compute Δy and dy for the given values of x and Sketch a diagram showing the line segments with…

A: Given: Now,

Q: Find the length of the curve r= e2θ, 0≤θ≤2

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Q: O Find the length of the following curves 4/2 3/2 + Dx, 0<I<1, 3 i) y(r) = 21 ii) 1 = ² + 21, y=…

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Q: Find at the given point without eliminating the parameter. dx2 1?, y = , X = 2 t = 2 3

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

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Q: When finding the orthogonal trajectory of the family of curves y = k x³, we dy get dx 2x y Зу 2у 3x…

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Q: 2. Find the area of the smaller loop of the curve r = = 3( 1- 2cose)

A: We will solve the following

Q: Use Green's Theorem to evaluate -1 (y? tan a?) dx + (3.xy + 4x – In(y² + 4)) dy, where C is the…

A: The green's theorem states that "line integral over a closed curve C…

Q: Consider the curve given by y2+xy=x3-(2y/3)+(3x2/4) a) Find all the points (x,y) on this curve…

A: Given is the equation  y2+xy=x3-2y3+3x24..............................(1) The objective is to find…

Q: 7. Find dyldx given the following implicit equation: xy-yx dy 1-2xy dx 2x y-1 dy dx 4xy-1 a. c. 1.…

A: Given: x2y2-y=x

Q: -0.08. Then evaluate dy for a=-3 and dz *+1 %3D Let y = dy = %3D

A: We have to find

Q: Find the value of d-y/dx at the point defined by the given value of t. x- 6t 2 -3, y= t 5, t=1 3D1…

A: Take the derivative than eliminate the extra terms as required.

Q: xy dx + (x2 + x) dy, where C is the path in the figure below with vertices (-5, 0), (0, 5), (5, 0)

A: Given data:     The given integral is: The coordinate of the first point is: (x1,y1)=(-5,0). The…

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 the length of the curve given x = (y/4)2 - 2 ln (y/4), 4>= y>=12.

A: The arc of length of curve is given byL = ∫y0y11+dxdy2dyhere y0=4 and y0=12 Given function…

Q: Evaluate ∮C(yexy−sinx)dx+ (xexy+ 1)dy where C is the path r(t) given by x=t,y=π/2(t−1)2 from t= 0 to…

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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

Q: 1. Which of the following first order is linear? 1 A. dy 1 dy et y-x) dx dy + xy = ey 1 C. y-x) dx…

A: