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Q: x+y uis = 1 n upi = no • prove that x-+ y-

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Q: OLet @ = (0,1)n Q = {x€ @104 x<1}. Prove that %3D 2) 2000m

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Q: Sin (n+))x Conv. unif nナノ on Prablem (5) Is the senies

A: The given series is: ∑n=1∞sinn+1xn+1 The given interval is: 0,π

Q: Q4/Find Loplace transtorm of £(4)= et by using} defining fanotion ر م ) ) st e" dt

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Q: Let fr)-ll for x0, then/(x) is Selact one A-1 * CNone of these DNot defined E1 a.

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Q: Assume that the coefficients in the expansion f(x) = anx" n=0 satisfy Enanx" – E Anx"+1 = 0. n=1 n=0…

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Q: Expand using Taylor upto four termns f((ntaih Ynt a k) senes

A: We will use some basic knowledge of Taylor series expansion of functions of 2 variables. Recall that…

Q: Is it possible to find a number  n  such that is ∫0∞  xn dxconvergent?

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Q: Prove that if Y:nz+P(x- mz) So thdz

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Q: b? – a? x dx 9. - Proof Prove that 2 a

A: This can be proved using Fundamental theorem of calculus. The second part of the theorem is used.…

Q: find the poin ts of discontinuity of the following func tion s : (a) g (x,y) %3D (b) f laiy)

A: g(x,y) = 11-x2+y2The point of discontinuity is where g(x,y) approaches ∞. Or the denominator of RHS…

Q: 9f d prove metric on x then that de de7ined by als is d (x, ) is mateic on x

A: The solution to the given question is explained below.

Q: Prove by the indirect method: Given: AMPN is not isosceles Prove: PM + PN

A: Concept used: Step of indirect proof: First assume opposite of conclusion of the statement. After…

Q: Find the d. c. of from definition.

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Q: Show that F(n fla)] ds pleae do it frast

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Q: In r dy If y , then is cosh z

A: Straightway proceed to differentiate both sides,

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

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

Q: Given: LM NO; ZLMO = ZNOM Prove: LO NM

A: Using Side angle side test,

Q: E/Prove the foltowing Eoshtutv)= CoshucoshVt Sinhu Sinhk

A: To prove that cosh(u+v)=coshucoshv+sinhu sinhv

Q: ) Let z be a c complese number then cos ( 58+2) is bounded in C2

A: Since, sinz and cosz are unbounded on C. These are unbounded along horizontal axis .

Q: To prove that dx In /1+ (In x)² + In x + C x/1+ (In x)2 we use the substitutions

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Q: x is the distance 1:- Show that the from morm Il x|l o7 2 to

A: We have to show that x of x is the distance from x to 0 Hence, x can e written as x−0 x=x−0 The…

Q: Suppose m is a positive f& La(μ), 11 £1100 2o and 2n = Ln Prove that = √ 1+1" 1₂" (n=1₁2,...)…

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Q: 57. Use the substitution u = x/3 to prove dx 1942=tan 1+0 www C 9+x² 3 3

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Q: 1f itwas x25ect, yatunt prove Thut dy

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Q: Show that the following cosh 3 (0,0) r(3,5) x² y?. (10xdx +6ydy)

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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: For for any pestive integor n Show that %3DFHE nth fibonacci term fn=the

A: We need to show that , for any positive integer n ,  f1 f2 + f2 f3 + ....... + f2n-1 f2n = f2n2…

Q: . Given: LM NO; ZLMO= LNOM Prove: LO NM Reasons

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Q: 6. so be it r = 3xi + yi – 2zk and f (r) : -- where |r| = r find all of grad(f) and div (-)

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Q: What is the expansion of f (z) = Ο Σ OE(-1)"z"

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Q: Consider (Ru) .f : R->R -3 X3o 3. X70 Prove Pex) is Con tinuos onR-301

A: Given that                                      f:R→Rf(x)=-3; x≤03    ; x&gt;0 we have to prove that…

Q: 2) f(x, y) = e xy %3D

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Q: Let 54 where Xey EA a Prove That RB equivalonce ceblion on Al Determine ll Idis tinct equi valance…

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

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Q: .If o + S CR is bounded above, then S has a supremum

A: It is given that S is a non-empty sub-set of R and R is bounded above.

Q: 3. ncnt) use PMI to prove that E

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Q: Find the sum of (arctan(n + 1) – arctan(n)) if exists. Lütfen birini seçin: a. b. 3 2 d. e.0 DOO

A: Given- ∑n=1∞arctann+1-arctann To Find- The sum of the above expression.

Q: Use Euler-Maclaurin's formula to prove that E n %3D

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Q: AB is tangent te OC at point A. mod

A: Given : AB is tangent to the circle at the point A. ∠ABC = 37°

Q: (c) Evaluate d Gosh: where C: |z| = 2 by using Cauchy's residue theorem.

A: Given integral is ∮C dzcoshz;   C : z=2 As, we know  If z = x+ iy then z =x2+y2 As given that  z=2…

Q: Find the lenegth of the cunde 312 2 from x=o to -

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Q: 2. Use the met hod of undet er mined coefficients to solve t he syst em x' = Ax+f, where - -] b. A =…

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Q: show that fE Riemann [o,!] and Find f de

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Q: let 9: R-R be given by grs) - Sin (는) %3D %3D dis prove that se second hind has prove of dis…

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Q: Let flx)= a cose + 3 Sinse with (o,f to)), (,2) and (T, 2 ). Use Muller's method to find a quachatic…

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Q: Let X be a rs from Exp(0). Construct a (1 - a) CI for 0.

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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.