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Q: 4. Show that z = a' Zax if z = e-al cos(x-at) %3D

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Q: EX/ show that im Cosy-1

A: Given limit is : limy→0cosy-1y To prove  limy→0cosy-1y=0 Use the trigonometry formula,…

Q: 2. Prove: cot2x - csc²x = -1 %3D

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Q: branch of z1/5 that is not continuous and positive on the imaginary axis?

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Q: Q2] Find the lower bound of Iz - 3|if |z - il < 1

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Q: Find Fxxyyy for the funcetion Fary]=j+JEnx-x]

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Q: () = 2 sec(a O conon1 O pton 2

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Q: Hiw- prove that %3D

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Q: 1. The first approximation of the root of xlogx - 1.2 = 0 in [2,3], by Regula Falsi method (False…

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Q: - Show that charactaristic function associatel with two distinct chavacteristic values always…

A: We have to show that the eigenfuctions/characteristic functions associated with two distinct…

Q: b)Show that, 6(z, 3zy – y' and (z,y) = -+3ry are harmonie

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Q: 1 If f(x,y,z)= of then x-y-3-

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Q: 0.2 Differentiate In x+1, with respect to x. x²-x+1

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Q: 4) State the Rank-Nullity Theorem.

A: To state: Rank - Nullity theorem.

Q: Find дхду of z = In(x² – y) %3D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Show that |1 - (x, + x,) - (x, + x,) X,*z = (x, – ,) (x, – y2) (x2- ,)(x2 - 2) 1 -(), + x2) 1 - (y,+…

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Q: Prove %3D 11

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Q: Prove of disprove if the given DE is exact. 2x^2 +4 =2(3-x^2y)y'

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Q: : Does fcz) = Continuous af cis

A: We have to solve given problem:

Q: Prove inf { ñt nEN}= %3D

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

Q: Calculate x - z. (Image 24 JI 8х -2 2x +1 3z z + 22

A: As per the guidelines I am supposed to do the first question among multiple questions. So I am…

Q: If C, C2 Cn are Constovts 1-1 . a,, uzXz) ---- Un (X)ave livffen antiable 4111 funetions at x with…

A: Introduction: The differentiation of a function y=fx is defined as f'x=limh→∞fx+h-fxh This is…

Q: Use moment generating functions to show that if X3 = X1 + X2, with X1 X3 - X V3 > vı, and X1 and X2…

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Q: Use linearization to approximate In(1.2).

A: we can use the following formula for approximate calculations: f(x)≈L(x)=f(a)+f′(a)(x−a). where the…

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

A: we have to find the limit of the expression

Q: (b) State Heine-Borel Theorem.

A: (Heine-Borel Theorem). A subset A of R is compact if and only if A is bounded and closed (with…

Q: Suppose csc(4) = 2 where A terminates in QIV, and sec(B) = -3 where B terminates in QII %3D

A: Given that                                     we have to find value of…

Q: Show that x + is increasing on [1, 0).

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Q: I need help doing number 7

A: We start solving the given equations simultaneously.

Q: 16) 1. ZDX 2. -X Show Your Work Valid Invalid

A: We have: Z⊃X~X ∴~Z    This can be written as Z⊃X∧~X⊃~Z  Here, p⊃q means "if p then q" This argument…

Q: 17. Use Theorem 4.7 to prove that Vx + 3 2 V3 + x/4 for

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Q: 4. Sketch the proph of the following funcfions; メーメ+4 (x+4 a) f(x) = (x+4) x b) gex) = %3D

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Q: Find the Reat teng th of sides of the triungle (AB Al4, 6,0), BL-6, 2,5) yclo, 9,5 ).

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Q: Verify Eular's Theorem for z=ax²+2hxy+by2

A: According to Euler theorem,  x∂z∂x+y∂z∂y=nz Where n is the degree of the homogeneous equation.

Q: 8-JIE FCx²_ ye, y-z²) =• then Prove that + Xそ 2Z

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Q: 2- (a) Using [X, P] = ih, show that [X, PJ = 2ih& and [&, Þ³1= 2ihP. (b) Show that [, p2 = 2in(in +…

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

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Q: 4. Prove: -| s|x - y| Vx, yER

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Q: Find leng th of the Cardioid Vsa6 from e -oto0 - 1 %3D

A: Use the formula of the length of the polar curve. L=∫0πr2+drdθ2dθ Here, r=aθ3 and drdθ=ddθ(aθ3)=3aθ2…

Q: 29 - For uhat values of a and b is ax+2b x+3a- b くXS2 3X-5 Continuous at every X ?

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Q: Show that cothx x+1 In X-1,

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Q: If f(x)=sin-'x. Show that (1-x2) fx(x)-xf (x)=0. HENCE ,prove that f^(n+2)(0)=n²f^n(0)

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Q: eturns ABC XYZ 0.2515 -0.22 55 0.4322 -0.28 45 -0.14 33 0.3144 -0.0645 -0.51 14 0.33 78 0.5534 0.68…

A: Covariance and correlation are two important concepts in financial analysis.

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.