Q10. Calculate the integral ſ F dr, where F(x, y, z) = (2x²lny) i + ( + z³)j + 2xzk and C is the curve with parameterization r(t) = ti + t²j+ tk with 1 ≤ t ≤ 2e without using the Fundamental theorem of line integrals.

Q: Evaluate the integral |(2e' – 2x) dy +(2xy +1) dx using Green's theorem where C is C 64 ans:-- 3…

A: Using Greens theorem the integral over a closed path can be converted into a corresponding surface…

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

A:

Q: = (1 – t)i + (4 + t)j ess your answer as an ir erical answer only.

A:

Q: Evaluate the expression a+b a+b when a=23a=23 and b=45b=45. Write in simplest form

A: # the expressions are printed twice , taking them once given a=23 and b=45 The value of a+b is as…

Q: Find the f(z) = u(x, y) + j v(x, y) for which X b) u = e cosy most general analytic function

A:

Q: Find the function f if. Vf-(3a²y + y², a² + 2xy), Vf dr with and without the Fundamental Theorem of…

A:

Q: The line integral P F.d7 can be evaluated using Stoke's Theorem where F = (2x, -3, 1) and C is an…

A:

Q: Let f(x, y, z) = 5x³ - y³ + z². Find the maximum value M for the directional derivative at the point…

A: Our objective is given below:

Q: F(x, y) = (4x³,3y²) along a path from (0, 0) to (2, 6). Find S F · dř. a) using a parabolic path. b)…

A:

Q: Is there a twice differentiable function f R2R whose best adratic approximation at the point (1,0)…

A: Given problem is from differential calculus in several variables. We have shown that there exists a…

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

A:

Q: Let C be the curve represented by the equations X = 4t, y = t², (0 ≤ t ≤ 1). In each part, evaluate…

A:

Q: Consider the following. C: counterclockwise around the circle  x2 + y2 = 49  from  (7, 0) to (−7, 0)…

A: Given,   C: Counterclockwise around the circle            x2+y2=49       from (7, 0), and (-7, 0).…

Q: Evaluate the line integral f, F . dr, where C is the curve given by F(t) = 3 cos ti+ 3 sin t j, 0<t<…

A:

Q: Let f(x, y) = x/y. Then the directional derivative of f in the direction of √2 point (1, 1) is ○ (1,…

A:

Q: Show that the function given by f(x,y)= x² + 3xy is differentiable at every poin using the…

A: Introduction: Distinctiveness (differentiability) implies continuity. If a function is…

Q: 6.(6 pts) Evaluate the line integral / (x+ y + 2) ds along the curve C given by r(t) = (sin t, cos…

A:

Q: Consider the tangent line to the curve r(t) = t2i −(1/(t + 1))j +(4 − t2)k at the point P(4, 1, 0).…

A: Given the tangent line to the curve r→t=t2i^−1t+1j^+4−t2k^  at the point P4,1,0. We have to…

Q: Let F = e'i+(xe' -e')j- ye'k and cbe a smooth curve defined by Then the value of the line integral…

A: The formula is  ∫F.dr=∫F(r(t)).r'(t)dt Here…

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: F. dr where F = yzi + xzj +xyk and C is the curve x = t, y = 2t², z = –2t² with 0<t < 1.

A: Given F=yzi+xzj+xyk and r=ti+2t2j-2t2k Now the vector field along the curve can be given by…

Q: Find an equation (x(t), y(t), z(t)) of the line that is the intersection of tangent planes at (1,…

A:

Q: Calculate the length of the curve given by the position vector function t r(t) = t? ( costi + sintj+…

A: We will find out the required length of curve.