C₁: r₁(s) C₂: r₂(t) C3 r3(u) = = = (s 2)i+ (2s² - 1)j + k 2t² i + (3t+7)j + (t+1) k (SER) (t = R) (u²+ 4u + 3)i + (u² + 6)j + (u + 2) k (u € R)

Q: Find u v, uu, ||u||2, (u v)v, and u. (2v). . u = 5i + j - 9k, v=i4j + 5k (a) (b) u. V u u (c) ||u||²

A: According to Bartleby's guide line we only do first three parts of multi-part questions.Given,

Q: エ+1 dx (7² +2x)

A:

Q: Find u x v, v x u, and v x v. u = 5i + 9k v = 2i + 9j – 4k. (a) U X V (b) (c) v x v

A:

Q: (c) Write (V3+ i)" in the form of x+ iy.

A: Here I have applied De Moivre's Theorem. See the solution.

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) × r"(t). P(C) = 21²1 - 48 + ²P²H 2³k r(t) 3 (a) r(t) 3it…

A:

Q: b)- dx a(13-x)(2+hncr)) + Ja9 differentiating on both sides dy (13-2) (2+dnc) da b9 de + be9) %3D de…

A:

Q: Solve Fyy + 3 Fxy + 2 Fxx = 2x, F(x, 0) = -x, 2, F(x, 0) = 0. F(x, y) =

A: General solution is given by complementary factor + particular integral.

Q: Əw Əv 2 y Find when u = 0, v = 0 if w=x + + ₁ x= x=5u-5v+1, y = 6u + 6v - 6.

A: To find the indicated partial derivative

Q: f(x,y) = Find f(3,4) 2+2u

A: Given Fuunction in x and y is as follows

Q: Find the solution. d3x d?x d³x dx + 2 =0 dr3 dr? dt

A:

Q: 3x + 11y af If f(x, y) = then is : 3x – 11y dy - 66x (3x + 11y)² 66x (3x – 11y)² 66x (3x + 11y)2 66x…

A: Partial derivative

Q: aff (² Find (3x + 2y)dA where D = {(x, y) | x² + y² ≤ 25, x ≥ 0}

A:

Q: f(x, y) = fx ( - 2, 2) = 2 2 3x² + 5y²

A:

Q: fx(2, 2) = fy(2, 2) = # f(x, y) = x² + 4x¹y.

A: