Z = X, + X, + at X1, X2. are NC

Q: prove if x → y then xor y = y =

A: To prove : If x→y then x or y = y Lets use the help of truth table to prove the above statement.

Q: Find fx, fy and f z if f(x, y, z) = e*yz In zx. %3D

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Q: if z=xarctan(y/z), find ∂z/∂x at x=0, y=1, z=1

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Q: ху f(x,y,z) =- х+у+z

A:

Q: Let f(x, y)= x'y+2x² and find f.(1,2) and f,(1,2) %3D 3x- y 1.

A: The given function is: f(x,y)=x2y+2x23x-y

Q: Give the condition which ensure that Je-| < 1 where z E C.

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Q: "he pmf of X is 4.x – 1 - fx(x) = where x = 1, 2, 3 %3D %3D to

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Q: Find the Fourir for fcae) = (1+x) [-x, ] %3D

A: Given function is fx=1+x and −π,π We have to find the Fourier series of fx. The Fourier series of fx…

Q: Compute f, aL a2f and :f(x, y) = (x + y)(2x + y)² ax' ay дхду

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

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Q: of af and Let f(x, y, A) = xy + A(5 – x – y). Find· ax' əy` af

A: f(x,y,λ)=xy+5λ-λx-λy .....(1) Differentiating (1) partially with respect to x, ∂f∂x=(1)y+0-λ-0…

Q: Find the fowien senies fon | X), -T<X <A

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

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Q: Let A = {x E Z: 8x} and let B={rEZ:12lx}. Then * ACB ВСА None of these A=B

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Q: Show that Plx-1,y) = A(x, y) X+ y-1

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Q: Show and use d(Xn, FCN))<« d(Xn-1 'x) Vny? To prove X = fx) %3D

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Q: DE : -t de dyx= 3et dt with indial conditins : xl0)=6 yl0)=1

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Q: Find all positive integers x, y, z satisfying x · y · z² = 5xyz. '*

A: Introduction :Given , positive integers x,y,zwe have asked to find the values of x,y,z which…

Q: Find ƒxx ( x, y)  and ƒxy( x, y).

A: Given, fx,y=3x+yx-1. The objective is to find fxxx,y and fxyx,y.   fxxx,y is found as follows: First…

Q: Prove that d (sec"x)= 1.

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Q: Let f(x ,y, z) = x²yª + z³ and x = 4s?, y = 2st?, and z = 3s?t. %3D %3D

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Q: Find the real numbers x,y,z,t if -3x +y+ zt = 0 3x + y(t – 1) – z(t+ 1) = 0 3x +y+ zt =t+2 - 3x +…

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Q: Sketch the set of points satisfying: |z - 1 + 2i| = |z + 3 + i|

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Q: Prove that da(x) = a(b) a(a), %3D |

A: This is a problem from Reimann Stieltzes Integral

Q: Integrate: Show that B(p+1,q)+B(p,q+1)=B(p,q).

A:

Q: Prove that dl = (Vu) x (Vv) - do.

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Q: Is 1z = 1 for all z ∈ C?

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Q: Making use of the fact that ˆα = y − βˆx and βˆ = SxySxx, show thatni=1[yi − (αˆ + βˆxi)] 2 = Syy −…

A: Given

Q: Let x, y ∈ R. Suppose x2 + y2 = 0. Prove that x = 0 and y = 0.

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Q: Find дхду of z = In(x² – y)

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Q: Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find ∂z/∂t.

A: Solution:- The given question is  Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find…

Q: prove that 16 x (I+x) dx 306

A: The product rule of integration states that∫fxgxdx=fx∫gxdx-∫f'x∫gxdxdx.

Q: Y is neither on the interior, nor the exte Y lies in the interior or in the exterior of Y lies on…

A: In this question we will use basic of algebra. We will use basic concept of interior angle and…

Q: Let F I2). Evaluate JJaw as z² + y? 0

A: In the given question, the concept of the Divergence Theorem is applied. Divergence Theorem Assume S…

Q: (c) Show that |(−1,1)| = |R|, where (−1, 1) = {x € R : −1 < x < 1}.

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Q: Prove if X,Z, y > 0 xy (3x +2y – 4z)+ yz(y+3z – 4x)+ xz(x+2z –- 4y)>0 then

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Q: ди Ifu=r(x* +2yz,y* +2zx)Prove that (y -zx) +(x² - 3z) + (:* - xy) ZX

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Q: Calculate f,e,5 as if f(x,y, z) = z In Vxy

A: here we have to find the functional value

Q: Show that u(x,t)= f((x+a*t)+f(x-a*t))/2

A: Given PDE is utt=a2uxx subject to ux,0=fxutx,0=0 We know that the general solution of the PDE is…

Q: xy Let z . Then: 4x2 – 5y? | az dz ду

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Q: Find all triples of integers (x, y, z) that satisfy x² + 2y² = z2.

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Q: Let C: |z-i=3 and I = §. dz 2z dz. Then %3D

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Q: Find f,, fy, and f, for f(x,y,z)= 5xy+ 3xz + yz.

A: It is partial derivative

Q: əz əz +y show that x 3z x²y2 B. If z əx ду %| x+y’

A: B). From the given function: z=x2y2x+y And x∂z∂x+y∂z∂y=3z As we know that the Quotient rule:…

Q: Use Green Theorem to Evaluate y x²dx – x²dy where C is left half of x² + y² = 25

A: Note that left half of the circle x2+y2=25 means the second and third quadrants. Now, in the second…

Q: a) If z= xy – xey/= , show that x * + y = xy+ z.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let z = 2 - 3xy?+ x². Zay %3D Zyy

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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: Use Green Theorem to Evaluate |y x²dx – x²dy where C is left half of x² + y² = 25

A: