Integrate f(x.y) = x +y over the curve C: x?+y² = 9 in the first quadrant from (3,0) to (0,3). Jex+y) ds = D (Simplify your answer.)

Q: Evaluate the line integral curve C : x = 4 cost, y = 8 sint (0 ≤ t ≤7 < NOTE: Enter the exact…

A:

Q: If y = Vx(3 – x)², show that- dy (3-х) (3-4x) Find the x coordinates of %3D dx all points on y =…

A:

Q: Integrate f(x,y) = x + y over the curve C: x2 + y? = 9 in the first quadrant from (3,0) to (0,3).

A:

Q: The approximation of I = xe" dx using Simple Simpson's rule is:

A: According to the fundamental theorem of calculus ∫abf(x)dx=F(b)-F(a), where dFdx=f(x). Simpson's…

Q: Find dy/dx and d-Y/ dx" of x = 2t" 3, y = 1. Give the equation of the tangent line at t = 2.

A: We have to solve

Q: Evaluate the line integral (8x + 7y)dx + (2x - 7y)dy along the curve C: a = 8 cos t, y = 16 sin t (0…

A:

Q: dy Differentiate parametrically to find dx in terms of t: x = 4t?,y= 2t3

A:

Q: dy +y = sin (;) cos t, %3D dt2

A:

Q: 2. Find the equation of the tangent plane and the normal line at the point (0 ,1 , 2) on the surface…

A:

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

A:

Q: Evaluate the line integral / (7x + 3y)dx + (2x – 8y)dy along the curve C: x = 8 cos t, y = 16 sin t…

A:

Q: integrate ƒ over the given curve. ƒ(x, y) = x3&gt;y, C: y = x2/2, 0 &lt;=x&lt;= 2.

A:

Q: Differentiate: y(x) along the curve xy =ex Show all working out.

A:

Q: Evaluate the line integral / (2x + 4y)dx + (2x – 9y)dy along the curve C : x = 4 cos t, y = 8 sin t…

A: Solution is given below:

Q: Why does this work? If we have the curve in the xy-plane: F (x, y) = 0, then why is the implicit…

A:

Q: Evaluate the line integral / (7x + 5y)dx + (3x – 9y)dy along the - curve C: x =2 cos t, y = 4 sin t…

A:

Q: Find f. fy for f(x,y) = xcosy + %3D x5 siny3 ey

A:

Q: Find dy/dt of y = Ssin (cost) and simpli -t -cos t cos t V1-? the

A: Given:- y=sin(cos-1(t))  To find:- y'

Q: Let y=sin(2x). If Δx=0.4 at x=0, use linear approximation to estimate Δy.

A:

Q: 2. Find the equation of the tangent plane to f(x,y) = sin(x² +y) when x = 0, y = T. 3 and r - cost

A:

Q: Evaluate the line integral curve C: x = = 4 cost, y (5x + 7y)dx + (3x − 6y)dy along the = 8 sint (0…

A:

Q: What is the equation of the curve whose tangent line passes through the point sec (In x) dx? (1,2)…

A:

Q: What is the value of the line integral ∫ AB y dx + x dy, if x = 3*t, y = 4*t + 4 and 0 ≤ t ≤ 1?

A: I am solving this in step 2

Q: Xyz f(x.y.z) = function is given dt P(2,t,) in point fax + fy + f2z colculate.

A:

Q: : Find the derivative of f(y, z) = ze2y + cos(2zy) at ppoint (9,1,0)in the direction of V = 2i – 3j…

A: This is directional derivative, just write the formula and solve accordingly.

Q: Assume that y = 5x and dx/dt = 2. Find dy/dt.

A: Consider y = 5xApplying derivative with respect to t on both sides and plugging the values:

Q: Evaluate the line integral (2x + 6)dx + (5y+ x)dy along the curve C: C F(t) = tỉ + 2tj, 0<t<1.

A:

Q: Find the moment of inertia with respect to x-axis the aarea bounded by 2y^2-8y-16x=0 and the line…

A: The moment of inertia is the rotational analogue of mass. The expression for moment of inertia is…

Q: Evaluate the line integral curve C′ : x = 4 cost, y = 8 sint (0 ≤t≤7) NOTE: Enter the exact answer.…

A:

Q: Find dy/dx for the curve x^2y^3 - y^2= x+y at the point (2,1)

A:

Q: Integrate f(x,y) =x -y over the curve C: x² + y = 16 in the first quadrant from (0,4) to (V8,18 - y)…

A:

Q: Compute xe" dx + x?y dy along the curve x 3t, y = t2, 0 < t < 1.

A:

Q: Integrate f(x,y)=x²-7y over the curve C: x² + y² = 64 in the first quadrant from (0,8) to (√32.√32)…

A: Draw the given equation of the curve x2+y2=64 and the given points. The given curve is between…

Q: Evaluate the line integral / (3x + 7y)dx + (2x – 3y)dy along the curve C: x = 6 cos t, y 12 sin t…

A:

Q: dy Differentiate parametrically to find dx in terms of t: 1 y = 2t2 + 4 X = |

A: x = 1/(t-1) y = 2t2 + 4 We have to find dy/dx

Q: Find the point of intersection of the tangent line to v=sin(2r) at y=0 and the line %3D x+2y=5.

A:

Q: Use the Linear Approximation off (x, y) = ex2+Y at (0, 0) to estimate f (0.01, -0.02). Compare with…

A: By the method of linear approximation, if we are given a differentiable function f in two variables,…

Q: Evaluate the line integral [(x + 7y)dx + (2x − 3y)dy along the curve C: x = 4 cost, y = 8 sint (0…

A: line integral

Q: Let sin(r-y) ||| + \y| +0 (x, y) = (0, 0) f(x, y) Is f continues at the origin? Why?

A: Solved below

Q: . Use fourth order Runga Kutta Method to find y at x=0.1, given that dy = 3e* + 2y , y(0) = 0 and h…

A:

Q: 3. Evaluate the line integral sin(y) dx + (x cos(y) – sin(y)) dy, where C is the straight line from…

A:

Q: Evaluate xy dx + (x+y)dy along the curve y = 4x from (- 2,16) to (- 1,4). xy dx + (x+ y)dy =

A:

Q: Find the equation of the tangent plane to z = ln(2x + y) at −1,3

A: Find the equation of the tangent plane to z = ln(2x + y) at −1,3

Q: Evaluate the line integral (2x + 4y)dx + (3x – 9y)dy along the curve C : æ = 2 cos t, y = 4 sin t (0…

A: We need to evaluate integral.

Q: What is the integrating factor of (ry + y) dr + (r + 2y-1) dy %3D

A: Given xy+y2dx+(x+2y-1)dy=0Compare above differential equation with…

Q: Find the rate of change f(x, y) = In(2a² + 5y2) at (v2, v2) in the direction making a (positive)…

A: First we have to find the divergence of the given function.

Q: ds Find where Vt +s = 2s . %3D dt

A:

Q: (b) Calculate the rate of change of the function f(r, y, 2) = ryz along the path r(t) = (sin(t), e“…

A:

Q: dy Differentiate parametrically to find dx in terms of t: %3t2, y3 6t

A:

Q: Integrate to find the length of the curve. 8 S = 2 - + 4t dt 4 + 8 2t ++) dt = (? +t ln(t) 1 II

A: