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: 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: 2. a). Find the velocity and acceleration of a particle whose position function is x(t)=…

A:

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: 6. Where does the tangent line to r = at the point (1, 0, 1) intersect the y-z plane.

A: Given:

Q: Find the length of the curve described by y = V sec* t – 1 dt, - sI 4 4 (a) 4 (b) (c) (d) 2/2 (e) 1

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: Let P be the curve that follows the helix r = from (1,0,0) to ( 1/2,√3/2 , π/3 ), and then returns…

A:

Q: 4. a) Find an approximation for f (x, y) = at the point (1.97,1.02). V10-r-5y b) Check Euler's…

A: (a) Approximate f(x,y)=410-x2-5y2 at the point (1.97,1.02) (b) Check Euler Theorem for…

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

A:

Q: What is the linearization L(x, y) of a function f (x, y) at a point (a, b)? How is L(x, y) connected…

A: Linearization L(x,y) of a function f(x,y) is given by the formula

Q: The percentage of female high school graduates who enrolled in college is given in the table below.…

A: Let x represent time(in years) since 1970, and let y represent the corresponding percentage of…

Q: How would you evaluate |F-dr, where C is the curve with param etrizati on r(t) for astsb?

A:

Q: Evaluate the length of the curve x = 6 – Vy – 2 , 3< y<6

A: To find the length of following curve  x = 6 - sqrt( y - 6) 3 ≤ y ≤ 6

Q: Which of the following is/are points on the curve y-x Br+ 22x - 24x +9 whore the tangent line is…

A: We need to find the points on the curve where the tangent line is parallel to the x-axis.

Q: (47) Let C be the curve y = 5x where 1 ≤x≤9. Calculate the length of C.

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: Let f(x, y, z) = 36xz - 14y² and let C be the curve given by r(t) = (1, 42, ) for (1) for 0 ≤1 ≤2.…

A: Given that the function                           and  for .To find the value of

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: dy = (x- 2)²(x-3). Determine The slope of a curve at any point (x, y) is given by dx whether the…

A: Since you have posted a question with multiple sub-parts, we will solve only first three sub-parts…

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…