Prove that f, uv v • dỉ = – §̟ vũu • dĩ

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: 2. Show that by using MEAN VALUE THEOREM . u-v < tan-1 v - tanu < if 1+v2 u-v 1+p2 0< u<v and ded…

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Q: Show that [x, p;] = iħ.

A: note :  As per our company guidelines we are supposed to answer ?️only one question. Kindly repost…

Q: Show that F = ху, , zy) is not conservative. 2

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Q: 6. Use an appropriate substitution to prove f(r)dr = f(a + b – x)dr. %3D

A: We have to prove definite integral property.

Q: show that }I f,lm) Ck-m) 2.

A: For, ∑m=0kf1mf2k-m, substitute k-m=n or m=k-n: ∑m=0kf1mf2k-m=∑k-n=0kf1k-nf2k-k-n…

Q: ). Show that V - u -ly- tan' u < V - u 1- if 0<u<v, < tan 1+v? 1+u 4 2< tan 4 25 3 and deduce that 3…

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Q: Find the projesiin Fisi+2j intro - Scaher componet

A: The vector equation is F=5i+2j. The vector equation is v=i-3j

Q: If I, = [x^tan"x dx, Prove that (n+1), + (n-1),,2 ° п 1 %3D 2 n

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Q: Estimate the value of f, (1 – r 4.r + 2x) dr using single application Simpson's 1/3 Rule.

A: This is a Numerical Analysis problem.

Q: Find fry for f(x, y) = In(x – y).

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Q: Assume X, Y CU. Prove that (U \ X) U (U \ Y) = U \ (X n Y)

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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: Prove az - ae that d az dz

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Q: 2)Evaluate exdA ,Ris bounded by y = x² ,y = 1

A: By using Fubini's theorem we solve the given problem.

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

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Q: find the fimet Qurtal dernratives 7 respect to rarraes X,4,Z.

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Q: Prove: If f1, f2 € R(a) on [a, b] with fi < f2, then ' fi da < s' fz da

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Q: If f(x) is continous on [a,b] then f(x) is differnitable on (a,b). True or False?

A: False Any differentiable function must be continuous at every point in its domain. The converse does…

Q: 2), Compute SE. di where Fュく-,) C is s shown

A: The general form of a vector valued function in three dimensions is given by F→=F1,F2, where F1 and…

Q: 74. Show that if 0 < x < y, then Vỹ - Vx < Vy – x.

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Q: Prove that: sec a + sec(120° +a)sec(120° – a) = –3 sec 3a

A: To prove that  secα+sec(120∘+α)sec(120∘-α)=-3sec3α

Q: 2. (– 13 + 3i)31

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Q: Let f(z) = (9 sin z + 2 cosz)tan¹z

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

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Q: ove that 1 cosh(tanh) = -1 -1 < r < 1. V1- 2

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Q: 6. Prove: 4 |x – y| 0, then x = y Vx, yER

A: To solve Q.6 Prove: If x-y&lt;ε, ∀ε&gt;0, then x=y ∀x,y∈ℝ If (Given) Then (To prove) ∀ε&gt;0,…

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

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Q: Prove that CP PS AM BN 9. MQ NR

A: Consider the equation

Q: Use the difinition of error function Prove that: 5(1/₂/2) = 5T let: ere (x) = 33/3324 dt

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Q: Let f(x, y, z) = x³ – yz?. Find af af of and ax' dy az

A: Given : fx,y,z = x3-yz2

Q: Q: Prove that tim x"- a" %3D

A: we have to find the limit of the expression

Q: Verify that the conclusion of Clairaut's theorem is valid, that is, that uxy = uyx u = x4y3 - y3…

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Q: Let f lany) prove that' flany) di f feren tiable I5 not point lo,0) .

A: Let the function be fx,y=xy Note:  [ We can say that f is differentiable at (a,b) if f is…

Q: prove that dv v 21/12 الله duz 2 2

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Q: Ju 20²u c² of2 (r, t) = u(x,0) = 0, ut(x,0) = 0 u(0,t) = 0 u(1,t) = 0. da2(x, t) + XX , 00,

A: Introduction: The basic method to solve a partial differential equation is the method of separation…

Q: Suppose u, VE Vand ||u|| < 1 and ||v|| < 1 . Prove it: V1- ||u||?/1- ||u||2 <1- (u, v)|

A: Suppose u, v∈V and u≤1 and v≤1 We have to prove that 1-u21-v2≤1-u,v Here, we have  u≤1 and v≤1 Also,…

Q: Let f = f(x, y), x = s +t and y = s - t. Show that (9- ) - se se as at ax ду

A: It is given that, f=f(x,y), x=s+t and y=s-t. Show that, ∂f∂x2−∂f∂y2=∂f∂s·∂f∂t.…

Q: Theorem 5 there is auniqe Reul for X=2 Sit X ER

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Q: (X), E(Y ) EXY), Cov(X, Y) , σχ, σχ and Py.

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Q: Prove that −(−v) =v

A: To prove: --v=v

Q: Prove that S. 8 dx √π 2

A: This question is related to integration using gamma function.

Q: ion Prove that for

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Q: Evaluate f(322 + z)dz from z = 0 to z = i.

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Q: 3 tari' (xty) , Prane that x2+ ydz Sen 2z be

A: We have z=tan-1x+yx-y This implies tanz=x+yx-y Let u=tanz Then we first need to find the degree of…

Q: J Prove (An B)' = A' U B'.

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Q: Prove that Srxdr = 2[, , da, r × dr =

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Q: Prove using soundness (Required): (∀x)A → (∀x)B ⊬ (∀x)(A → B).

A: The proof is shown below.

Q: Construct AB congruent to XY

A: Given query is to construct congruent segments.