[&+2y)dx +(x² - 3y°)dy (3+2 4. Evaluate where C is any smooth curve from the point A (1, 0) to the point B(2,-1) В(2, —

Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

A: Given: x=et……1y=te-t……2 where t≥0   To find: Slope of line tangent at x=3

Q: 2: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G(x, y) = x³y² + y² sin…

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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: 1. Consider the curve C: r(t) = (t - sin t)i + (1– cos t)j, 0StS 2. %3| | (a) Find an equation of…

A: Since solve the first question for you. If you wanting any specific question to be solved then…

Q: The position of a particle in the xy-plane at time t is r(t) = (t+2) i+ (t- + 3) j Find an equation…

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Q: Find the equation of the tangent plane to z = ey + x + x2 + 11 at the point (5, 0, 42).

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Q: (3+2.xy)dx+(x² – 3y² )dy 4. Evaluate where A (1, 0) C is any smooth curve from the point to the…

A: We use Green's Theorem here, which says: ∫CP dx+Q dy=∫∫R∂Q∂x-∂P∂ydR...(1) where C is the smooth…

Q: Consider the curve in the xy-plane repre- sented by = e' and y = The slope of the line tangent to…

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Q: 4) Consider the curve given by: cos(xy) = x(y – 7) – 1 %3D Find y' dx a)

A: Given function is cosxy=xy-π-1 Chain rule of differentiation states that: ddxfgx=f'gx·g'x…

Q: 3.) Calculate the curve integral f (1 – a² + y²) dx + (1 + x² – y°) dy. Here C consists of the…

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Q: 17. The equation of the tangent line to the curve y = at the point (3, ÷) is 2 A. x+16y+11= 0 B.…

A: As this is a multiple question according to the Bartleby Answering rule, only first question is to…

Q: Find dy/dx and d²y/dx² at t = 2 for the parametric curve x = ½t², y = ⅓t ³.

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Q: Find the maximum height above the xy-plane of a point on r(t) = (e1 , sint, t(4 - t))

A: Maximum height above the x-y plane will be the maximum value of z .So we will take z parameter of…

Q: 4) Find the x-intercept(s) and y-intercept(s) of the curve x = 3t – 3, y = sin t

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Q: 1. Calculate the derivative dy/dx for the plane curve defined by the equations…

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Q: Evaluate y dx + x dy along the curve y x² from (0,0) to (1, 1).

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Q: The curves C,:x=t, y=t, z=t, t20 and C,: x= sint, y 1+cost, z=1, 120 have intersection at the point…

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Q: 7. a. Find the points on the curve x = 3(t2 – 3), y = t³ – 3t where the tangent is horizontal or…

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Q: I need help with 1a)

A: straight line becomes y=x

Q: dy in terms of t: Differentiate parametrically to find dx y= 2t2 +4 t - 1 X = A [4t(t – 1)²] В…

A: Given :x=1t-1y=2t2+4

Q: (ii) Find the length of the curve y = E* from x = 0 to x = 2. %3D

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Q: 3. For the function h(x, y) = x2 + y2 - xy+x find h and h, and then find the tangent plane to h(x,y)…

A: To solve the following problem, We use the standard formula of differentiation and  after that we…

Q: For the curve y = f(x) = x², 0 ≤ x ≤ 2, its length is 2 L = 1+ dy dx dx =

A: Given curve y=f(x)=x2,0≤x≤2 The objective is to find the length of the curve.

Q: .: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G (x, y) = x³ y² + y² sin…

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Q: Q.3 a) Verify Green's theorem for |(x2 + 2xy) dx + (y? + x³y) dy Where c is a square with vertices…

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

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Q: 20. The curve 2x2y+ y 8x +1 passes through (4, 1). Using the tangent line to the curve at the point…

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Q: 3. The length of the curve determined by the equations x =t and y=t from t=0 to t= 4 is a. b. 2[VF…

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Q: 3.) Calculate the curve integral (1 – x² + y²) dx + (1 + 2² – y²) dy. Here C consists of the curves…

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Q: Find the value of the derivative dy/dx at  t=2π/3 when an object moves according to the parametric…

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Q: A heat-seeking particle has the property that at any point (x, y) in the plane, it moves in the…

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Q: Evaluate the line integral. { 4) ( y2 dx + x dy; C is the curve x =t2 - 1, y = 4t, 0 st s 1

A: The given line integral is ∫Cy2 dx + x dy; C is the curve x=t2-1, y=4t, 0≤t≤1

Q: Find the equation of the tangent plane to z = ey + x + x² + 7 at the point (5, 0, 38). = Z |

A: To find the equation of tangent plane to z=ey+x+x2+7  at the point 5,0,38In general the equation of…

Q: If a curve f(x) has dx dy = (y – 1)2(2+ x) and passes through the point (-1,2), then what is the…

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Q: (dy = arctan dx, (i) Use the facts: dy and (dy/dt) to find dt d dx (dx/dt) ds (ii) Use the fact that…

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Q: 1. If F(x, y) = (3+2xy)i + (x² – 3y²)j. Evaluate F. dr, where C is the curve given by r(t) = e'…

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Q: Find the equation of the tangent line to the parametric curve. x = t1/2 y = t2/3 at t = 1. Also…

A: The curve is defined by the parametric equations as x(t) = t1/2 and y(t) = t 2/3   Apply the chain…

Q: dy in terms of t: Differentiate parametrically to find dx 1 y = +2 t+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: (2² + y² – 1)³ – x²y3 = 0, 2- Given the curve dy find dx -2 2

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Q: (il) Find the point in which the tangent line to the curve F-12-30)1+ 2+Int'+ k at t=1 intersects…

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Q: 8. Find parametric equations for the tangent line to the curve r(t) = (t² +3t +2, e' cost, In(t +1)…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Q4] Find the equation of the tangent plane and normal line to the surface z + 8 = x ey cos z at…

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Q: 2. Find for the curve dx x²y3 – 2xy = 6x² + 2y³ + 1 -

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Q: 3. Find the value of c such that the line y = x + 3 is tangent to the curve y = cvx. C =

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Q: The x- coordinate of the point on the graph of y = yx – 1 at which the tangent line is perpendicular…

A: Topic- application of derivatives

Q: 1. Calculate the derivative dy/dx for the plane curve defined by the equations: x(t)=t²-4t,…

A: Given that: x=t2-4ty=2t3-6t

Q: dy Assuming - 9x³ - 2y - 7xy = 0 defines y as a differentiable function of x, use the theorem Fx to…

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