If A= xe Z:2" = 1 and B = {x e Z:-4 < 3x-1<11}, then find n(A×B),where Z is a set of integers.

Q: If z = e'x + y In(x), find z, and z, Zx Zy II

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Q: H) 9f zyzec then prove thal nl x=4=Z, (alogen) %3D

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Q: Q2= A) for E= 2xĭ-3Y3+K %3D prove That divc curl È)=0 %3D

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Q: Let R be and bl#0) = iff a with unity - Let a l#0) in R- Show that and b an I.D are are associates-

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Q: If f(z, y) – e . In(9y) , then fz is given by: O - 9e In(9y) o - 27 e In(9y) O 9 e In(9y) O 27 e…

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Q: . Find x(t) = Σo ant such that tx" = x' for t > 0 when x(1) = 0 and x'(1) = 1. in=0

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Q: a²z If z = In(x² + y²)., find ax2 ay?

A: Here we have;  z=ln(x2+y2) ...................(1) partial derivative with respect to x

Q: 2. Show that 4=x i+y°j+:'k is irotational.

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Q: 10 a- Let X1, X2, ..,Xn~N(0,0) and T Find %3D X2 E (T),Var (T)

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Q: A continuous r.v. F(x1= === 2 × -IN 15 X has CDF X Co OBX C1 18X 16 17 **** 18

A: Given: Fx=0            x&lt;012x        0≤x&lt;1k            x≥1

Q: dy Find Z for y = (8+ x³ In x)ª + e3x

A: We have to find out derivative

Q: 1 prove that | e -ym dy = mr(m) -ут

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Q: -2 Let f(t,y) = y + 3t?e'. Then f satisfies a Lipschitz condition in y with L = 2, given that 1<t<2.…

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Q: -ALef xe Rbe Such thad Xn→x, show that Yn = xi %3D 4 X.

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Q: Let f(x, y,2) = x² sin y+y e", where x =t +3,y = ne*-1 and z = In 2t. at t = 1 is: -2 1+2n O -12n…

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Q: If f:(0,∞)→Rf:(0,∞)→R is defined by f(x)=xln(2x)f(x)=xln⁡(2x) for every x∈(0,∞),x∈(0,∞),  then…

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Q: (a) Suppose x E Q with x # 0 and y E R – Q. Show that their product ry is irrational.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Let z(x, y) = xe* + sin xy + y - In 2 then a a) -In 2-2 b) In 2-2 2 c) 2 (²-1) d) - 2 (²+1)

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Q: HW klx) = 2x+5 ㄱ 1. Find ke-¹(x) 2. Prove by kokorklok

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Q: Suppose that F(s) = ℒ{f(t)} exists for s &gt; a ≥ 0. Show that if k is a positive constant, then…

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Q: Compute analytically convolution of x(t) and h(t) defined as follows: S 1, if 0 <t< 2, { 0,…

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Q: Q4 Prove that E(",") = ("::)- () .n 2mzr. %3D +1 +1

A: we have to prove that                                                   ∑k=0mn-kr=n+1r+1-n-mr+1 now,…

Q: Suppose that a) b) f(x, y) = [15x²y; 0<x<y<1 0; otherwise. Compute E(X | y), Var(X) and Var(Y).…

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Q: 9 Give with an not example of T: W≤X →Y, to XT Ext. .R. boundedag. - keše bes

A: Please find the solution innext step this is an non-example of Tietze extension theorem in Topology.

Q: If y is a solution of y(x)-[(x-1t)»(?)dt = 1, then which of the following is true? (a) y is bounded…

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Q: In the given figure, X > K. Prove that WY> JL. K X Y W

A: Here , we have ∠X&gt;∠K we have to prove that WY&gt;JL

Q: If z =e* + In(xy) Evaluate- ,and ,at the point (1, 2). Hence, calculate the change in z when x…

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Q: t²x"" +2tx" + x' +2022x 0 for t> 0. If their Wronskian satisfies W(2) = 20, then find W(t) for all t…

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Q: If u=l0g Cx +ytz- 3>yz) prove that Ce+y+z) he

A: Given that u=logx3+y3+z3-3xyz Then  ∂u∂x=3x2-3yzx3+y3+z3-3xyz ∂u∂y=3y2-3xzx3+y3+z3-3xyz…

Q: 2) Show that L(1-x*)P",)P"mx) dx = 21(1+ 1) Sim 21 +1

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Q: dz Find if yz – In z = x + y ax

A: To find the partial derivative of z of yz-ln z=x+y with respect x, differentiate yz-ln z=x+y, while…

Q: SSS zdV Q3: Evaluate E + y² + z² = 1 and x² + y² + z² = 4 in the upper where E lies between the…

A: We have to evaluate the integral ∭EzdV, where E lies between the spheres x2+y2+z2=1 and x2+y2+z2=4…

Q: Find y' if exy = e 4x -esy-

A: NOTE: Refresh your page if you can't see any equations. .

Q: 2. Derive a formula to approximate S* s* f(x;y)dxdy yo xo Using Simpson's rule with x2 – xo = 2h ,…

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Q: Suppose that x2 = y2 = e and yz = zxy. Show that xy =yx.

A: Since, yz = zxy

Q: In GL(2, Z,,). det

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Q: Suppose that ƒ € H(C) and f(n) = 0 for all n e Z. Show that all the singularities of f(2)/sin(rz)…

A: Given that fz is an entire function with fn=0 ∀n∈Z and let gz=sinπz We have to show that fzgz has…

Q: Let M, = Z, – Z;-1, Zo = 0, where {Zn, n21} is a martingale. Show that E(M,„Z„-1] = 0

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Q: If f(x) - g(x) = 1, then f and g have the same antiderivative. %3D O True False

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Q: Find fCx) if flo)=0 and the tanGat (k,F CX) has ine af Slore x(x+2) a

A: Given for the function F(x), F(0)=0 and tangent line to F(x) at x,F(x) has slope xx2+23.

Q: H. If g(z) e2*z In , compute g'(r). What techniques should you be using in this %3! case?

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Q: 2. Use a theorem to find the ff. Zx if yz? + z = 5xy – 1.

A: Find out the zx when function is given as yz2+z=5xy-1 or yz2+z-5xy+1=0

Q: If f(x,y,z)=z In(x²ycosz), then fz is O 2z X OZ y O2z y O In(x²ycosz) - ztanz <|N

A: This question is related to partial differentiation, We will solve it using given information.

Q: Given F(x, y) = (2xe'6(y), e'x²(eY + 0(y)) with o E C'(R) then O (A) F is conservative only if o(y)…

A: (A ) is true.

Q: Let flt.v) = v+3t°e'. -2 -y + 3t2e'. Then f satisfies a Lipschitz condition in y with L = 2, given…

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Q: Find f, and f and evaluate each at the given point. F(x, y) = e*y?, (In 4, 2) f(x, y) f,(x, y) =…

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Q: Suppose that a) b) f(x, y) = [15x²y; 0<x<y<l 0; 0; otherwise. Compute E(X|y), Var(X) and Var(Y).…

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Q: Suppose that x2 = y2 = e and yz = zxy. Show that xy = yx.

A: Assume that x2 = y2 = e and yz = zxy.  Now from  yz = zxy we have  yz-1 = zxy-1z-1y-1 = y-1 x-1 z-1…