Consider the relationship R CN x N, R(x, y) holds iff (/a /9) E N. True or False R is reflexive true false

Q: (c) Suppose that o is differentiable. Prove the identity | øVø •n ds : (OV²ø+ V¢ • V¢) dA

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Q: f z x dA, D= {(x, y) |0 < x < m, 0 < y< sen x} 9. D 10. | x dA, D= {(x, y) |1 < x < e, 0 < y< In x}…

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Q: ди ди ди for u = az Find p-q if p= x+ y+ z ,q = x + y + z ,r = = (V3,2,1). and ax' əy 9-r x + y - z…

A: Q3. Given that                                            u=p-qq-rp=x+y+zq=x+y+zr=x+y-zPoint, (x, y,…

Q: Let /:R'R. S(x. y.2) = (e' tan y,x' In y). Compute D(f).

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Q: Find where 1)let . V°g r = l7| -- g(r) = In(r³) s = xi + yj + zk * vo x Vp 2) find = yz + zx2, P =…

A: Gradient and cross product

Q: X,X, X3 R.S. T3 %3D Bind dis tribution of Xo

A: Solution

Q: (c) For any (a, y) E R?, let F(x, y) = (4x - 3y + 1, 3x +4y + 1). Then F is a similarity.

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Q: Given f(x, y) = x° + 2xy³ – 2y", find fz(x, y) = fy(x, y) =

A: Given  f(x, y) = x6 + 2xy3 - 2y5.

Q: The linear approximation for f(x,y)=Vy+cos?(x) at (0,63) is O L(x.y)=(65+y) 16 L(x,V)=(65-y)

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Q: now if we take F (x, y) = (ax, ay), where a is any positive constan %3D

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Q: af Given f(x, y) = In(6x² + 8y²) then %3D

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Q: Given that f"(x) = cos(x), f'(T/2) = 8 and f(T/2) = 7, find: %3D f'(z) =O %3D f(2) =U

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Q: Let f (x, y) = 9e2xy what is fryx (x,y) =? %3D

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Q: (a) (x² + y² + z² + w?)3/2 = 4

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Q: Given f(x, y) = 3® – 3xy - 2y, find fz(x, y) =| fy(x, y) = %3D

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Q: Let f(z,y) = z* + y° – 2r° - 4y be given. Which of the following statements is correct? %3D

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Q: Let cov(X,Y) = var(X) = and h(y) = }* (4y, 0<y<1 %D %3D 45 45 elsewhere Then the value of var(2X +…

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Q: Given f(x, y, z) = 5x² + 3y? + 2z², find fr(x, y, z) = fy(x, y, z) = %3D f-(x, y, z) = %3D

A: We have to find partial derivative

Q: Given f(x,y) = ex cos y, Evaluate fx(2,0)

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Q: Let X and Y have the joint p. d. f. f(x, y) = {*+y for 0<x,y<1 otherwise f(x,y) %3D Then P (Y|X = )…

A: Let X and Y have the joint pdf fx,y=x+y      for   0&lt;x,y&lt;10            otherwise Then we need…

Q: Given f(x, y, z) = V 4a? + 2y? + z², find fz(x, y, z) = fy(x, y, z) = f:(x, y, z) = |

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Q: Use the Chain Rule to find- af when r = 2, t =-1 of the function ar f(x, y, z) = e3xyz cos 2xyz ; x…

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Q: If f(x, y, z) = In(x7 + y +2)+V + y + z), then find fr, fy and fz at (1, 1, 1). %3D

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Q: f({x, y))) for all c e R and all (x, y) E R?

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Q: prove. that s U. W V- W 1. U.r V.r

A: Using the vector triple product, it can be written that: a→×b→×c→=a→·c→b→-b→·c→a→. Using the scalar…

Q: Need help on showing how to prove this      (x(y+z))w=(xy)w+x(zw)

A: Expressions are mathematical statements that have a minimum of two terms containing numbers or…

Q: Prove that c?p?-(jx² + jy²+jz³) is the invariant quantity equal to c?po?.

A: Consider the provided question,   Prove that c2ρ2-jx2+jy2+jz2 is the invariant quantity equal to…

Q: Explain how the evaluation for each of S. f(x, y) ds, ſ. f(x, y) dx, ſ. f(x,y) dy, and F ( x, y) · d…

A: We have to evaluate each integral. They defines as follows-

Q: Let z = e*y, where x = Vuv and y = . Find in terms of u and v.

A: Change the z in the terms of u and v and the differentiate.

Q: Consider the relationship R C N x N, R(x, y) holds iff (/æ /T) E N. True or False R is irreflexive…

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Q: Given f(r, y, z) = – 5e 4ayz, find %3D fr(x, y, z) = f,(x, y, z) = f:(2, y, z) =

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Q: Gy Let Px) = x²/3, x. thens Rx) = x2/3 ×シ。 then: %3D O Find ê cx) ? 2 Gruphs off R and f

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Q: . Evaluate F dr, where F(x, y) = ryi+z'y²j, and C is given by r(t) = ti+tj. 0sts1.

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Q: If f(z) = 6tan(z) , then f'(r) = (A) In(6) 6tan(2) (B) sec2(z) 6tan(2) (C) In(6) sec2() 6tan(z) (D)…

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Q: R and r are defined by E(r, – 5)(y – T) Sry VS., Syy SSR R2 r = SST' (1) Show R? = r².

A: If y = a+bx is the linear equation  Correlation attempts to measure the strength of the relationship…

Q: Given f(x, y) = 3x° cos (y"), find f-(r, y) = fy(x, y) = fae (x, y) = fyz (x, y) =

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Q: PART C dy 12. Show that dx 2 for the relation %3D V%3D10, x, y X. # 0. y

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Q: -. Evaluate f. F dr where F(x,y, z) = e²i + xzj+ (x + y)k and C is given by r(t) = t²i + t°j- tk, 0…

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Q: Given f(x, y) = x® + 3xy4 – 2y°, find f-(x, y) = fy(x, y) =

A: If f(x, y) is a function then, fx(x, y)  is differentiation of f with respect to x making y variable…

Q: If z = f(x, y), where x = 2ts and y = t2 + s², show that () - 2 + 2x + 4y %3D dsdt

A: Here given z=fx, y and x=2st, y=s2+t2

Q: Given f(x, y, z) = x In(yz³), find fay and fyz. %3D

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Q: If // f(x,y) dA > 0. then f(x, y) ≥ 0 for all (x, y) in D. D

A: answer is in next step. please give a like !!

Q: Given f(x, y) = – 6x- 2xy-by°, find 3 %3D f-(z, y) = fy(x, y) = %3D

A: Solution: The objective is to find the partial derivatives

Q: Find . for (x,y) = x² + y² af af ду' дх Find ду' дх Je Je for f(x,y) : sin xy? x2+1

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Q: Consider f (x, y) = re63ry f-(x, y) = e63ry and fy(x, y) = %3D e63ry

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Q: af when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y ,x = 2t + s, y = 2s – t. a) Find as

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Q: f(z) =z? is discontinuous

A: f(z)= z2 is a polynomial function in z and polynomials are continuous everywhere.

Q: If f(2) = sin(z?) = U(x, y) + iV (x, y), determine U and V. Verify that the C-R

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Q: Find the are length of f(r) = (r + 3)2 from r = 0 to x = c in terms of c. %3D 2/3

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.