Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = 5t²1 – 3tj + 3t³1 (a) r(t) (b) r"(t) (c) r(t).r"(t) (d) r(t) x r"(t)

Q: If z = x² - xy + 3y2 and (x, y) changes from (3,-1) to (2.96,-0.95), compare the values of Az and…

A:

Q: 3-2 P. (4a² b)x3(ab ³) ==

A:

Q: = f(2y + 3)²√√y+2 dy

A: To solve the given integral

Q: dx (4-2²)° (뿌): O none of these 1/2 11/8

A:

Q: explain geometrically what Q(x, y, z) = 1 represents

A: The equation Q(x, y, z) = 1 is a general form of a three-dimensional equation. The geometric…

Q: (x-2)² + (y+1)² =16, find- A. 16 (y+1)³ d²y dx² B. 16 (y +1)³ C. 16 y³ D. 16(x-2)² (y+1)³

A:

Q: (2t+1)(2t-1) dt. 4. S

A:

Q: Derivative of y = 16 is: a) 1 b) 0 Derivative of f(x) = - 6x + 2 is: a) - 4 b) 2 Derivative of g(x)…

A:

Q: f(x y, z) = x2 - 8y5 + z -4. Find (-3, 1, 5) for O a 1 O b -4 10 O d -5

A:

Q: Find * 1 y" if y =-(x -3x)

A:

Q: C) Find S x2e-* dx

A:

Q: then find x²°u +2x)y əxəy If u = (x – y)f(y/x), a2u then find x2 dx2 a2u + 2xy дхду

A:

Q: Evaluate (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (3, -7) 21

A:

Q: +: 1+ x² ]dx

A:

Q: 2 (0² 20 0 Ans v=c₁ +c+.

A:

Q: (X²y² + 1)dx +2x²dy =0 use the substitute xy=u

A:

Q: Evaluate -42 (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (3, -7) X

A:

Q: If y = (5x+ 1)(2x- + In x), then will be dx A. (5x + 1) (+;)+5(2x-1+ In x) В. B. (5x + 1) (-) +…

A:

Q: Ho Find (yor dy d'y ) and (y or -) for the following functions: dx dx L 2. y= x² (x-1)² 5. y=(x²…

A: We need to find the first order and 2nd order derivatives of the given functions.

Q: If fxy (x, y) = , ,0 2) =

A: Given,fXY(x,y)=x+y27 ; 0<x<2 , 3<y<5

Q: 3x + 2 10. Find the principal value of dx. (a² +9)(x- 4)x

A:

Q: Evaluate (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (2, -7) 323 2

A: Here to find the value of line integral we consider two path c1 :from the point (0, 0) to (0, -7)…

Q: Uz + xuy = x²y, u ( x, 2x + = 5x

A:

Q: What is the value of x in (2x - jy) + (y - jx) = 1 - j5?

A: We have to find the value of x where 2x-jy+y-jx=1-j5

Q: Y = -2X, then p(X, Y) = 1?

A: Solution

Q: (xdx ydy + zdz)2z {(z²x²y²) (xdx + ydy + zdz) dz + %3D

A: Differential equation

Q: y? lim (х.у)-(1,0) х2 + у? — 2х + 1

A:

Q: If fxy (x, y) = y for 0 2X - 2) =

A:

Q: ,2 Vx3 + 2dx

A: Consider the given: ∫ x2x3+2dxApply u-substitution:u=x3+2∫ x2x3+2dx=∫u3du=13⋅∫udu=13⋅∫…

Q: Find // (3x + 5y)dA where D D = {(x, y) | x² + y² 0} . Round your answer to four decimal places.

A: Double integration

Q: Evaluate (2x - y) dx + (x + 3y) dy. JC C: x-axis from (0, 0) to (0, -3) and (0, -3) to (9, -3)

A:

Q: (x+6) 15. J (x+2)2 dx

A: Here I am attaching image so that you understand each and every step.