Show that (c + V² – x \c – V² - x. + V² – x²) – In = 2 In(c 2 In x

Q: Show that 1 п-1 .. 1 X2 x5 п-1 x2 ... =II("; – 2;) i>j 1 n-1 .. •.

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Q: 10 Prove that: ²x = 1 (g)(x) m = 1 so that the product

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

Q: x - x3 + x² – x + 1 is reducible over Q True False

A:

Q: Let X = {x E Z|x = Y = {y € Z]y = 3n for some integer n}. 6m for some integer m} and let %D a. Prove…

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Q: Prove that: V² (64) = $V²y +2V¢• Vy+yV² ¢

A:

Q: 5. prove thatS" erf (x) dx =o CA

A: ddx(erf(x)) =2 e-x2π   I =∫-aa erf(x) dxI= erf(x) x -∫ ddxerf(x) x dxI = x erf(x) -2π∫ x e-x2 dx-x2…

Q: 3. Prove that {12a + 4b |a, b e Z} = {4c\c € Z}.

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: 2) FIND THE INTERVAL OF CONV. * (x-1)^" 2 (n+i) n=0

A:

Q: Q1(i) Prove that 1 1 1 + 2n²+1 V2n2+2 V2n2+n]

A: To prove: lim 12n2+1+12n2+2+.........+12n2+n=12

Q: If u = x3 -3xy and v= 3x2y-y3, prove that Pu/Əx2 + Pu/əy2 = Pv/ax2 + Pv/@y²

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Q: 2- Let z=x+iy. Find a) Img(1/2) b) Re z c) Img (1/z')

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Q: 1] Let X,YER. Prove that VxVy(4x+9y>9⇒(x>5/4 Vy> 4/9)) using method of indirect proof.

A: Prove that ∀x∀y4x+9y>9⇒x>54∨y>49, where x, y∈ℝ. Prove the statement using method of…

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: Prove directly. a) [(Vx (p(x) → q(x))) ^ (3x p(x))] =3 x q(x)

A: When we prove logical equivalence, we use the truth table. But sometimes, the truth table becomes…

Q: x is even and v is any integer, then their produc

A: If x is even then x=2m where m is any integer y is any integer,  Case I Let y be even y=2n where n…

Q: Prove that Σ = 2" . a. x=0 b. = 0. x=0

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Q: Suppose X = (X1, X2, . .. , Xk) ~ Multinomial(n, p) , with p = (p1, P2, ..., Pk), prove that Cov(X;,…

A: Introduction :-  Given that X is a vector of random variable and it follows Multinomial(n,p) Where p…

Q: α Let V₁ = {(₁)|a € R}. V₁ with standard V4 operations will fail both axiom "close under addition"…

A: Let A be a set and ∘ binary operation on A then 1. We say A is closed under the binary operation ∘…

Q: What is t' (x) when t(x) = In( ): %3| 2x2+3x+2 Select the correct answer below: O t (x) = 2 + 4x+3…

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Q: Prove that i 224 s 2xP for xzO, y zo i and 1 t L-l with p>

A: Given that x,y≥0. And 1p+1q=1 with p>1. Consider gx=xpp+1q-x. Then g'x=xp-1-1 and g'x<0 when…

Q: Show that for all z1, Z2 E C, Then we have: |Iz1| – |z2|| < |z1 +z2l

A: 2) The inequality can be proved as follows:

Q: U prove that In (l+x)) 2.

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Q: Find the missing parts of the Wronskian: x Inx ? W = inx - and 4 O x2Inx and x3Inx O 1 and Inx O 1…

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Q: %3D n-0o 2n

A: Given. We are given a limit and we need to prove that the limit of the given function at infinity…

Q: Assume that |Xn] 0. (Hint: first, prove that P(|X|>c+1) = 0.)

A: Answer:

Q: Suppose x-j, for j-0, 1, 2, 3 and it is known that Find Po123(1.5). P₁1(x)=x+1, P₁2(x)=3x-1, and…

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Q: If x > 0, prove that T - In (1+ x) > 2+2x

A: Using derivative

Q: 3) Find integers x and y such that 13x + 15y = 1.

A: We see, 15 - 13 = 2              =&gt; k(15 - 13) = 2k for any integer k              =&gt; 15 k -…

Q: Prove indirectly: "V n E Z, 4 ł (n² – 2)."|

A: Ans:Let us assume that 4/n2-2;∀n∈zthen we have there exist a positive integer k such…

Q: Q) prove that (1) -2P xSinx 2.

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Find the smallest integer in the given set a.{ xϵ Z f x &gt; 0 and x = 4s + 6t for some s, t in Z }

A: Consider the equation: x=4s+6t……1   where: x, s, t∈ℤ and x&gt;0

Q: Q3/A/ Prove that ) + ",) = C). %3D إضافة ملف

A: As per our guideline we are allowed to do 1 question at a time. I think you hav already done 2…

Q: Show that f(x)= x14 – 6x + 75 is irreducible over Q.

A: Eisenstein's Irreducibility Criterion: Let us consider polynomial…

Q: 21. Find af and of if f(x,4)= 3x" +2xy+ Sy , x= 4v? + Bn", and u 2v-w? Vour %3D 4= 2v-w? Vour av…

A: We have to check

Q: Let x ∈ R. Prove that if x 0.

A: Given :

Q: Let r E Rt. Prove that if z – 2x2 +2 2021. -

A: Let x2=t, Now if x∈R+⇒t∈R+ ⇒t2-2t+2≤0⇒t-12+1≤0⇒t-12≤-1which is not possible for any value of t, for…

Q: Show that f(x) = x* + 2x? + 5x +1 is irreducible over Q.

A: The given polynomial of the function is f(x)=x4+2x2+5x+1 We have to show that the polynomial is…

Q: Verify that Al2 = I½A = A for an arbitrary A E M2x2(C).

A:

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: 4. Prove that d x" = nx"-1 ミクー! de

A: To prove that ddx(xn) = nxn - 1

Q: (a) Show that for x > 0, 1 5a' < In(1+ x) < |

A: As per guidelines, we will solve only first part. Kindly repost other part separately.

Q: use the convolution theorem to find L'{2+1 -1 4 Specifically s²(s²+1)

A: Given,        L-14s2s2+1=

Q: Find a mat rixP such that P [1 2 1 0 | 1 0 P = O A. -1 1 1 - ОВ. 1 P= OC. 0 1 -1 0 P = O D. 1 1 1 0…

A: Just multiply both sides by P from left side and set P as 2×2 matrix.

Q: Q1(i) Prove that 1 1 1 + V2n2+2 + V2n2+n] %3D ... V2n²+1

A: Here we find limit

Q: 2 O Expand Pn = 2x +3x +) in Term of P.f,.

A:

Q: 4. Verify thatf (x) = x³ – x2 – 20x + 6 satisfies the three conditions of Rolle's Theorem on [0,5].…

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Q: 3. Prove that (An B)² C A x B.

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Q: 1. Use substitution technique to show that ++x+2+x- v2 +C dr 1 In rV+r+2 +x+2+r+ V2

A: As per our guidelines we are supposed to answer only one question that is the first question. For…