Evaluate | G(x, y)dx | G(x, y)dy and | G(x, y)ds 2t, y = t2, where t is on the closed interval from 0 to 1 for G(x, y) = x³ + 2xy? + 2x. Round answers in the hundredths on the curve C indicated by x = place.

Q: *Gl0/ Apply Stoke's theorem to Cal cu late S4y dx +2zdy + 6y dz where c i$ the curve of xyt 2 = 6z…

A: Apply Stokes theorem to calculate ∫C(4ydx+2xdy+6ydz) where c: intersection of x2+y2+z2=6z and z=x+3…

Q: For the curve y = f(x) = x², 0 < x < 2, its length is 2 dy` dx - {(aV17+ In (4 + v17). VI7). L 1+…

A: Apologies for the inconvenience. The correct solution is given below: Given that y=x2 Hence, dydx=2x

Q: On what interval is the curve t2 X. dt y% = Jo t2 + t +2 concave downward?

A:

Q: Find dy/dx and d²y/dx². x = e', y = te¬t 1 - t dy dx t – 2 dx2 21 For which values of t is the curve…

A:

Q: Evaluate f. x'dz +z?dy +y?dx where C is the curve x = t ,y = t2, z = t? from t = 0 to t = 2.

A:

Q: compute f ds for the curve specified. f(x, y) = /T+9xy, y=x³ for 0 < x < 1

A: Line integral: If rt=x(t), y(t), a≤t≤b then, ∫Cf(x, y)ds=∫abfx(t), y(t)x'(t)2+y'(t)2dt

Q: Find dy/dx and d²y/dx². x = t2 + 7, y = t² + 9t dy dx2 For which values of t is the curve concave…

A: Here we have to differentiate the given parametric equation.

Q: 18. The length of the curve y = r* from r = 0 to r = 2 is | V1+2® VItz® dz B. | V1+3x2 dx A. C. D.…

A: Question 18 is solved. Solving more questions are against the policy of bartalby. In question 18 ,…

Q: Can you please solve these two sub problems and show all of the steps and say the correct letter

A: Since you have submitted two questions, we'll answer the first question. For the second question…

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

A:

Q: Given that dy =0 dx when x=1 for the curve y=x³+ 3x2 – 9x +6 d?y Find dx- and hence find which of…

A:

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: Cvaluate (xy) s ds where C is the curve y = x², for 0 < x < 2.

A:

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: 2 zy ら- Let Los 63 Z), find the Wニ Value of d at the point (!, Ln2, o) on the curve x = Cost , y =…

A: To find.  The value of dw/dt at the point(1, ln2, 0) on the given curves.

Q: At time t, the position of an ant moving in the xy-plane is given by parametric functions…

A: Given parametric functions are: dxdt=3t+2dydt=t2-4

Q: Find dy/dx and dy/dx2. x = t2 + 3, y = t2 + 3t dy dx dy dx2 For which values of t is the curve…

A:

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…

A:

Q: Q4. Let C be a portion of a curve from (2,0) to (2, 2). Let F(r, y) = (tan(2²) + e²", 2.re²y + cos…

A:

Q: dy for the curve defined by x° – y = 2xy? dx Which of the following is O 2x + 3y? 3x2 – 2y O 3x2 –…

A:

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: Compute f ds for the curve specified. f(x, y) = V1 + 9xy, y = x3 for 0 < x < 2.

A:

Q: Find the point at which the curve Sx=f +19 Ly=d-4t has a vertical tangent. (x, y) = (

A: Given: The curve is given as x = t5 + 19, y = t4 - 4t   To find: The point (x,y) at which the given…

Q: On what interval is the curve y = 0, v- [ t2 dt t2 +t + 2 concave downward?

A: NOTE: Refresh your page if you can't see any equations. . to find the inflection point, first, we…

Q: Find dy/dx and d²y/dx². x = et, y = te¬t dy dx dzy dx2 For which values of t is the curve concave…

A: We have to find derivative

Q: Given = (1 + x -- k) dy da 13 What is the value of k such that y is perpendicular to the curve y =…

A:

Q: Consider the one-form w = dx +g' (y) dy on R², where g : R →Ris an arbitrary smooth function. Show…

A:

Q: i) Find the length L of the curve y = x + cos x, 0<x <T/2 Use any one of the following formulas 2…

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: Find dy/dx and d²y/dx². x = e', y = tet dy dx dy dx2 For which values of t is the curve concave…

A: Given a parametric equation,

Q: :- 1 Find the interval on which the curve y = dt is concave upward. (Enter your answer using…

A: Given Data The integral is    The function of the integral in interval 0&lt;t&lt;x is,

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: 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: At the point (a, b) the curve T =t-4t, y=t2 +2t, t eR has a vertical tangent line. What is the sum a…

A:

Q: e the line integral Sc(3x?y+2)dx+ (x+3)dy where C is the curve r(t) = (t2, 3+t²) with 0 <t < 1.

A:

Q: Evaluate f, x*dz + z*dy + y*dx where C is the curve x = t,y = t, z = t? from t= 0 to t= 2.

A: x = t2 ,  y=t2, z=t2 dx = 2t dt,  dy= 2t dt, dz = 2t dt  Putting values in the integral: ∫02t4(2t…

Q: dy Assuming 3x +y-4xy 0 defines y as a differentiable function of x, use the theorem Fx to find Fy…

A:

Q: Find dy/dx and d2y/dx2. x = cos(2t),    y = cos(t),    0 &lt; t &lt; π   For which values of t is…

A:

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

A:

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

A:

Q: Let F = Vf, where f(x, y) = sin(x – 9y). Find curves C, and C, that are not closed and satisfy the…

A:

Q: Find dy/dx and d²y/dx². dy dx d²y dx² 11 || x = t² + 9, y = t² + 3t For which values of t is the…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: d²y + y = 0 cos x 2 dy a) Show that if y then + dx² x dx dy b) Find dx given y = sin vx c) Determine…

A:

Q: Consider the following x = 2 + t², y = t² + t³. Find the following in terms of t: 1) and enter it…

A:

Q: Find an equation for the tangent plane to the graph of f(x, y) V3+ r2 – 3y2 at the point P(2, 1,…

A:

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

A:

Q: Find dy/dx and d²y/dx2. x = et, y = te-t dy dx d²y dx2 For which values of t is the curve concave…

A:

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