13. Let F (x, y) = (1(²y²)x, af(x²y? , a(y²) Y) and suppose that C is a smooth curve parametrized a(x²) by R(t) where |t| 0. Show that F. dR = 0

Q: Calculate the length of the curve F (t) = (2t-1, t + 1) with t ∈ [1,2].

A: Given that  the curve F (t) = (2t-1, t + 1) with t ∈ [1,2]. To Calculate the length of the curve in…

Q: 21 Let F(x, y) = (3x + 2y)i + (2x - y)j. Evaluate F. dr where C is the curve X y from (0, 0) to (1,…

A: Here we calculate the integral along the curve x = y2 from (0,0) to (1,1)

Q: 13. Find an equation for the tangent plane of the graph of f at the point (xo, yo, f(xo, yo)) for:…

A: Note:-Since you asked multiple questions which are not interlinked to each other, according to our…

Q: Let F(t) = (- t + 1, t – 2t", - 2t). Find the line (L) tangent to r (t) at the point (- 15, – 24, –…

A:

Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

A: given ∫C2y+4zdx+2x+3zdy+4x+3ydz where C is the curve given by rt=t3,2sinπt2,3cosπt2 for 0≤t≤1…

Q: Let f(x.y) = ry. a. Sketch/describe the domain of g Domain = { (x,y)]yz0} b. Sketch a contour map…

A:

Q: Which of the following gives the length of the curve y x2 + 2x from x = 0 to x = 5 ? (x2 + 2x) dæ I…

A: Length of the given curve will be

Q: Compute F. dr for the oriented curve specified. F(x, y) = (4x2, xy), line segment from (0, 0) to (2,…

A:

Q: 6) What is the tangent plane of f (x, y) = 5x² – 2xy? + 3xy + 4x at point (xo, Yo) = (1, –2) ?

A: The question is solved in step. 2

Q: 3. Given F(x,y)=(y,2x), find F-T ds where curve C is the parabola y=x from point (0,0) to point…

A: We use line integration to evaluate this.

Q: Show that the tangent at P(x,y,) the curve Vx+ Vy = Va is yy,² +xx, ² = a²

A:

Q: The tangent plane to z = f(x, y) at the point (1, 2) is z = 3x + 2y – 5. (a) Find f,(1,2) and f,(1,…

A:

Q: Let C be the curve consisting of line segments from (0, 0) to (1, 1) to (0, 1) and back to (0, 0).…

A:

Q: Suppose you are standing on the surface z = ƒ(x, y) at the point (a, b, ƒ(a, b)). Interpret the…

A: Given that a person standing on the surface z = ƒ(x, y) at the point (a, b, ƒ(a, b)).

Q: Let F = (4x³ + yz, xz, xy). Let C be any smooth curve from (1, 1, 1) to (2, 3, 0) Calculate cF dr.

A:

Q: Evaluate [ f (x,y,z) ds given that f(x,y,z) =, and the curve C is ř(t) = 2ti +t²j+÷tk (1<t<∞) %3D…

A: Given: f(x,y,z)=x2xy+6yz r→(t)=2t i→+t2 j→+13t3 k→   1≤t&lt;∞

Q: 13. If F-xyi-y² j, evaluate [F-dr where C is the curve y=2x² in the xy-plane from (0,0) to (1,2).…

A: The given problem is to evaluate the line integral of the given vector field over the path C curve…

Q: . Evaluate SF.dr: ▪ F = (x+z)i +zj+yk. C is the line from (2,4,4) to (1,5,2).

A: Since all subparts are different and not interlinked so as per our guideline we are supposed to…

Q: 99. Determine the concavity of the curve x= 2t + In t, y = 21 – In t. %3D

A: