3.4 Compute the angle between -- ). --- 1 y = 2 using a. (x, y) := x'y TBy, 2 В:- 1 b. (x, y) := x 3

Q: 1. (1 - x)y' = y?

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Q: Demonstrate the following relationship involving the dot product and cross product (a) u. (v x W): =…

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Q: What is the value of t in terms r, s, and u In the equation

A: The solution is easy to see

Q: Consider the following. u = (2, 0), v = (5, 7) (a) Find u · v. U'V = (b) Find the angle between u…

A: Given that  The vectors  u=(2,0) and v=(5,7) To find the u.v and angle between the u and v

Q: 3 For V- , evaluate y' when y= 4. A) -4 B) 4 (c) -2 D) 2

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Q: еху (ay cosica) since) -y + ay²e²) dx = ) dx = (x - 5.n²cx) - 4xye Ja

A: Exact differential equation Mdx+Ndy=0 [ where My=Nx ] has the solution. ∫M (taking y as a…

Q: 11 a) Cari nilai dy dengan nilai x yang diberikan. dx Find the value of given the value of x. de i)…

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Q: 5. The angle between the tangent line and the normal line is (a) 180° (b) 90° (c) 45° 6. If x= 3t-2…

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Q: х — у—1 3y – 3x – 3y (1) = 1 у (1) %3D 1

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Q: 20. Let (). ()- u = v = If æu + yv = w. (æ, y E R), then a - y = (A) 2/3 (В) —3/2 (C) 3/2 (D) –1/2…

A: To find the value of x-y from the given vectors.

Q: d 1) Find sec dt 2)

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Q: OL. If w = f(u, v), u = cosx and v = sinx, show that: (30 Marks) %3D d?w dr v² fau + u?f- 2uvfuv -…

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Q: 16. Find the values of r so that the function y= e™ satisfies the equation y" – 4y' – 21y = 0. A)…

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Q: 2b). Let y* + 5x2y² + yx = 624. A) Find y'

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Q: 10. Given X(7,3) and Y(-6,2), find the coordinates of any point Z such that XZ XY = 41. .

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Q: dy de Xoy. -Secxy)

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Q: 2 a) y = Find y'. 3e (ax-5)4

A: Explanation and solutions is given below.....

Q: Given f(x, y) = sin(x2) + xy³, find Duf(x, y) where u is in the direction of (1, 2). What is Duf(-2,…

A: To find the directional derivative of given by function

Q: dw 21. : 1-cosw A. -tan w + secw + C B. w – cotw + C C.-cotw – cscw + C_ D. -cscw + tanw + C

A: We can find the integral value as below.

Q: 3. Find x and y so that NR 1 MQ. Find m/MSN. 5x (9y+18) S 4. If m/BGC = 2x - 5 and mzCGD = 4x - 13,…

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Q: 2. y = V4-x , x=0 and y=0 about the y- axis

A: Given that y=4-x2, x=0 and y=0 about the y-axis

Q: The roots of the characteristic equation of y"-7y=0 are:  a. √7.-√7  b. 0, 7 c. 7,7 d. 7.-7

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

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

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Q: Q1. If the line y = mx + c passes through (3,4) and makes an angle of sin-1 (3) with the positive…

A: If the line  passes through  and makes an angle of  with the positive direction of -axis, then to…

Q: Q2. If w = f(u, v) , u = cosx and v = sinx, show that: (30 Marks) d?w = v? fuu + u² fvv – 2uvfuv –…

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Q: 1 2 Y = -1 x = 3 using a. (x, y) := x'y %3D 2 1 b. (x, y) := æ' Ay, A:= 1 3 -1 -1 2

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