EXvyP(x, y) is true when there is an x for which P(x, y) is true for every y. A True B False

Q: If f(x,y)= Iny, then Vf(x,y)= :- Select one: O True False

A: We know that, gradient is a vector function. ∇fx,y=fxi^+fyj^

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: Ju ди ax2 at u(0,t) = u(10,t) = 0 u(x, 0) = x where temr

A: WE use separation of variables i.e to assume solution of form X(x)T(t) to find two ODE's .Solve the…

Q: Let x, y ∈ R and suppose for every ε > 0, we have x ≤ y + ε. Then x ≤ y.

A: Given:  the given statement is false eg.    let x=2, y=1  and ε =2 ≥0         we have y+ε=3 and x=2…

Q: Find all values of n such that y = xn satisfies…

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Q: dy(x) z = dr ving statements are false? ive of y with respect to r

A: The value is given as, z=dyxdx. The equation given follows , z is the derivative of y with respect…

Q: Let f(x, y, 2) = xe' + ye" + ze* and P,(1,0,0) then Vfle, is 2i + 2j + k. True False

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Q: x then ux is XX If u = V y %3D

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Q: Find all values of x and y such that Px(x,y) = 0 and P Py(x,y)=0 simultaneously. P(x,y) = 5x² -…

A: Topic = Algebra

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: af Given f(x, y) = In(7x² + 9y²) then

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Q: Let ƒ(x, y) = 4x2 - 9xy + 6y3. Find ƒx (x, y) and ƒy (x, y).

A: To find the derivatives.

Q: Find all values of x and y such that Px(x,y)=0 and Py(x,y)=0 simultaneously.…

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Q: Hewin If Z =R Cxxy]:and u=x-yg V=x²-y 그를 + show that

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Q: Q111f и %3D (1 —2ху + у?)""/2, Prove that: ди ди y əx y? u3 У ду

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Q: af (x,y) f(x, y)=xe"+* 5 у, Х (а) Сompute y af(x,y) X f(x, y)=xe³"+* ,5 у (b) Compute ду y

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Q: Find when r = 2 and s = 0, if: as z = xy² – x – y x = y = ers 1+s

A: Here given that z=xy2-x-y, x=r1+s,y=ers So, ∂z∂s=∂z∂x∂x∂s+∂z∂y∂y∂s        =y2-1-r(1+s)2+2xy-1ersr

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

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Q: Let R = Z[x] and let I =. Then I = R. True O False

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Q: Q.8 If v = (x² + y² + z?)¯/2, prove that a2v + ду? = 0. ax2 az2

A: We find second  the partial derivatives lf given function with respect to x, y and z and then add to…

Q: af axdy of f (x, y) = xy(x+y — 1) — x² Find-

A: The given function is: fx,y=xyx+y-1+x2   As we know that; The Power Law: ddxxn=nxn-1 The Product…

Q: Let p(x) = 5x² – 3x + 2 and suppose that y 1 0 A = |0 1 0 0 y for some y E R. Evaluate p(A).

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Q: VXEN, 3yEZ s.t. x + y^2 = x - y O TRUE O FALSE

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Q: Proof by contrapositive that for x, y ∈ Z, if xy is even then either x or y is even.

A:

Q: IT Evaluate v if y=xsinx at x = 6.

A: Giveny=xsinx

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

A: Given

Q: According to boolean algebra x.(1 + y) =?

A: We will use the following 3 rules : (i) Distributive law : a•(b+c) = a•b + a•c  (ii) Identity law :…

Q: Q3: A. Find Wer if W = f(x, y) {x = reost, y = rsint W₁,

A: From chain rule we know if w=f(x,y) and x=g(r,t) and y=h(r,t) then, ∂w∂r=∂w∂x∂x∂r+∂w∂y∂y∂r

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

A: We are given,  X1, X2... are independent random variables with E Xn=mn  and N∈P0(λ). The set is…

Q: {"q} puv {"v} f1 divergent then {an + bn} is divergent. are a true b) false

A: To find true or false

Q: of ALL explanatory variables x2, x3,

A: There will be various methods to test the significance of the exploratory variables in the…

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

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Q: Q: If u =f(x² +2yz, y² + 2=x)Prove that (y-ax

A: Step by step compute the derivative with respect to each variable x,y or z. Then substitute it in…

Q: Let x, y range over N and define Q(y): 3x. x < Y. Choose all the values for y such that Q(y) is…

A: We know that set of natural number is {1,2, 3,4,5,6,7,.......}

Q: Find for z = for z = ex-y Əz Əx

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Q: Additional Problem Prove the statement: 3X CZ such that Vx E X, 2 | x and 3 | x.

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Q: dr is divergent a true b) false

A: We have to calculate  ∫1∞1x2 dx.

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

A:

Q: If Cov(x,y) = 0, then X and Y are uncorrelated Select one: O True False

A: If two variables are independent then their covariance is zero and we, say that they are…

Q: If f(x, y, z)=√x²y² z², then fxyz (x, y, z) = 2xyz √x² 1² z² Select one: True O False

A: Given: if fx,y,z=x2y2z2 then fxyzx,y,z=2xyzx2y2z2 We have to state if the given statement is true or…

Q: Let X-(1,0,- 1,-/2)'. Then, ||X||∞ =V7 %3D Select one: O True False

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Q: prove using soundness that the converse of Axiom 2: (vx)A → A[x := t] is not a theorem

A: Solution: If Î" ` Ï• then Î" |= Ï•. Completeness If Î" |= Ï• then Î" ` Ï•. Thus, any formula proved…

Q: SU SW. Complete the proof that ASTW ASXU. T. V W Statement ZW ZU SU N SW ZS ZS 4 ASTW ASXU 2.

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Q: 3 We can de fine the fallaing tunction on real mumbers ( called "absohite value") ; abs (x) = x if…

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Q: xz, + 2yzy = 0, for r > 0, y > 0 yzz – 4xz, = 2ry, for all (r, y) #2, – ryzy = z, for all (r, y)

A: (A) Given the PDE xzx+2yzy=0 We will use the characteristic method to find the solution.

Q: -x+y<y. 2 If x < y, prove that x <

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Q: generally true? Prove / disprove this.

A: P(x+y|x)=probability of (x+y) given x. P(y|x)=probability of y given x.

Q: Let f(x, y) = x² + y2 + 2x + 4 and P,(-1,0) then Vfle, is i – j. True False

A: