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Q: How to determine The direchon that the arrow at the pout 6,1) at he eghahión of he 1t arder g'=…

A: find the slope of the equation  at particular  point Example : y'=y-2x Take x=  0     0      0     0…

Q: 5. (6 + 15i ) 3

A: this is a problem of complex analysis.

Q: The value(s) of x that satisfy In(x² + 1) – 2 In(x) = In(16) – In(8) are/is

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Q: prove that 2. catX+c

A: We use that- sin2x + cos2x =1  so that 1-cos2x= sin2x

Q: Show that : sup {reQ:r<a} =a, for each a e R. %3D

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Q: D. Prove that CQ = DQ 3. In the accompanying figure we are given that se(C) = without using any part…

A: In the question we have to prove that CQ=DQ

Q: SHOW that V Ź a? Jor a, E IR when His ineguaity e kold .

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Q: - Justify the last two steps of the proof. Given: RS UT and RT US Prove: ARST AUTS

A: Given that:

Q: - check the exi's tence of limol of the Lunetiom 41n at X= 1 %3D 2X+/ こ Xラ-3

A: To check: The existence of the limit of the function. Given: The function is fx=2x+1     -1≤x≤1x22-3…

Q: A, is skew-symmetric, then prove that (B B + B, B') An = . Ajk = 0. %3D

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Q: メ (myst メート→ Q(2,4) where: Path C くz rom ○)と to over the Evaluate the

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Q: If Z = eax + by F(ax - by); the value of %3D az is + a ду az

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Q: 16. Write a two column proof. Given: OSTUV U V. Prove: AVXS = AUXT T S 8.

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Q: 2. (– 13 + 3i)31

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Q: Let x, y E Z. Prove that if 3 ł x and 3 ł y, then 3|(2² – v²).

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Q: Let x and y be non-negative reab· show that, use Proof by Contradietion X+4 2

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Q: (6) If u, =*-!P«(x)Pn -1(x) dx, show that nu, + (n – 1)n-1 = 2, %3D and hence evaluate u„.

A: Given un=∫-11x-1PnxPn-1xdx

Q: Let W = Lin and U= Lin 2 (a) Show that R' = W U. Explain.

A: Note:- As per our guidelines, we can answer the first part of this problem as all the parts are…

Q: Let a and b be any real numbers. Prove that Cov (ax, by) = abCov (x, y).

A:

Q: Consider o Con Assume He holding holding Vo =Vi =d, thatis, to the ofter going 1. Draw the Pre

A: Hi, there! As per the norms, we are allowed to solve single question at a time when multiple…

Q: By using Caushy Riucman Prove that? e ae

A: We will use the following result :  Result : Let the function f (z) = u(x, y) + i v(x, y)  be…

Q: A, Az, An are independert,2) PLiln)=r9)-1), where Bi is eitler Ai or Ai for izlityn in please proof…

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Q: ) Prove that sac"()/T sec

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Q: (a, b) is measurable. ulgn O ihi O

A: I will use the definition of measurable set.

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

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Q: If (a + bx)e = x, prove that x’y, =(xy,-y)

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

Q: (a) Prove the following property: (:) - (.".)

A: Hey, since there are more than two questions posted, we will answer the first question. If you want…

Q: Prove that Z(D,) # {1} if and only if 2|n (hint: if 2|n look at ri).

A: Let us suppose, Dn=e,r,r2,..,n-1,f,rf,..,rn-1f and nis divided  by 2. Then, n2 is a integer. We see…

Q: Verify that the conclusion of Clairaut's theorem is valid, that is, that uxy = uyx u = x4y3 - y4…

A:

Q: Which postulate or theorem should be used to prove AHIG AJKI? G O ASA O SAS O SSS O AAS

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Q: cos (o,+ O>)+ ì s:in (8,+Ə.)) Prove this kW- Mon 183O

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Q: 12. Prove: ΔUΧΖ-Δ AUXZ AYVZ ~ Z.

A: Given: chord UXChord YVand the Center ZTo…

Q: 1. Prove with the usual notations that: (b) A + V =- (a) EV = VE = A (c) A= SEZ

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

Q: Prove that du Inlul + C where n= -1 u

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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: If ge R [a,6] 'ib h) < gcx) exapt gex) except for a finite number 8 points in (a, b] then prove that

A: The partition from a to b should be first divided to form a set of integrals.

Q: prove in words: If {X, Y, Z} ` A ∧ ¬A, then {Y, Z} ` ¬X ` = derivability

A: Use the deduction theorem: Deduction theorem states that, If ┌ A⊦B then ┌⊦ A→B

Q: Prove by unduclion Hhat if ne IN - 31,2,3,...f aud 9> 2

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Q: ve that the are lengh - loj secx from

A: Introduction: The formula for the arc length for the curve y=f(x) from a to b is given by,…

Q: and are 2 soihions and w Cy,,Y2)(to)to what con conclude ? we

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Q: Let A=(aij)nxn be symmetric and positive definite. Show that laul< (anan), , lis = 1,2,..n 9

A: Given: Let us consider the given, A=aijn×n Let's prove that aij&lt;aiiajj12,i,j=1,2,...,n.

Q: (b) Using Venn Diagram to prove that (A U B)e = A° N B° ?

A: To prove the following using Venn diagram A∪Bc=Ac∩Bc First consider the left hand side  Set A

Q: (a) Prove that if f e C (R²) then a (af af %3D

A: This is a problem of the calculus of several variables, higher dimensional calculus.

Q: Let X + 0, |X|> 2. Then (X, Tna) is not To -space. Select one: True O False

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Q: -Prove that (SeT)' S eT*. hore 0 is he zero linea the identity henaee of V Deo that 9)S. arifi that

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Q: To test this null hypothesis, we compute t using a special case of the formula. state the formula?

A: In this case, we need to write the test statistic formula for testing the null hypothesis.

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.