Show that In(x") = y In(x) for all x, y > 0, only using the rules of derivative for the natural logarithm and the fact that In(1) = 0.

Q: 3. Let A be a square matrix, and that k1, k2 and A are scalars. Show that if Av = Xv and Aw = Xw…

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Q: Let the given implication be: “The beach erodes whenever there is a storm.” Which of the following…

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Q: 1. Give an example of a 2 x 2 matrix with no inverse ( singular). Show how it become singular 2.…

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Q: Find the approximate root in 5th iterations of the function f (x) = x³- 2x - 5, xo = 2.5 by x = 2x +…

A: We have to find the approximate root in the 5th iteration of the given function musing Fixed-point…

Q: s+7 F(s) = s2 - 3s – 10

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Q: , How many ways are there to distribute r+s identical balls among five different children such that…

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Q: WHAT SYMBOL IS THIS

A: As the given curves are c1=3sin2θc2=3cosθ

Q: Let S be the quadric with equation 36x2 –4y² –9z² – 36x = 0. Describe the traces of S on the…

A: The given curve is 36x2-4y2-9z2-36x=0............(i)  To Draw: Its Traces on x-y, y-z, and z-x…

Q: 1) An electronic manufacturing firm has the profit function P(x) = - x3 +? x² – ADx + A, and revenue…

A: a. Given, Px=-BAx3+DAx2-ADx+A and Rx=Ax3-Bx2-Dx+AD. The relation between profit, cost and revenue…

Q: Convert the numeral to a numeral in base ten. DAF8sixteen

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Q: Figure Q2 shows a rectangular enclosure formed by a straight wall AB and a fence CDEF of length 10m.…

A: The area of a rectangle is calculated using the formula: Area=length×width. The double derivative…

Q: = Cos(x)+ sin (x)

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Q: Draw the graph of the following map: xn+1= {3xn if x1/3  Show also that the periodic orbits are…

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Q: [a b] There are exactly two orthogonal matrices of the form What are they? 1499

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: B. Find the adjacency matrix of the following graphs. 1. 2.

A: 1 Consider the given graph We have to write the adjacency matrix. The adjacency matrix for the given…

Q: y = 0.78540 + t sin t + 1/8 sin 3t could be used to express the instantaneous value of a waveform.…

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Q: i) find the relative extrema of ?; (ii) determine the values of ? at which the relative extrema…

A: Since 25-x2 is defined -5≤x≤5, the domain of the given function is -5≤x≤5. Substitute fx=0 in the…

Q: 2. A thin conical density of the s cone. Hint: set

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Q: List the solution: xi = x2 = %3D O x3 = T3 is not needed O x4 = %3D C4 is not needed

A: claim- find the maximum value of f and the set of variables that gives this maximum value.

Q: ne data represented in the box-and -wH O: Foot Lengths of Grad

A: This is a problem of finite math and Box plot.

Q: Solve the system of differential equations x' 7x + 4y - ly' — 8х + 5y - ¤(0) = 1, y(0) = - 1 x(t) =…

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Q: Given four trapezoids of width 1, calculate the size of the shaded zone.

A: Introduction: The trapezoidal rule, also known as the trapezoid rule or trapezium rule, is a…

Q: (2) Let ƒ : [-x, 7] → R be defined by 0 if – a<x< -, 1 if-플<z<0, 0 if0<x< T. f(x) = (a) Calculate…

A: We will use the basic knowledge of the Fourier series to answer this question correctly and…

Q: Find the area Inside the lemniscate r = 6 cos 20 and outside the circle r = 3.

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: functions" then site one 3. Explain the statement "All functions are relations but not all relations…

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Q: ) Determine whether the lines L and L2 are parallel, skew, or intersecting. If they inter- sect,…

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Q: Consider the following propositional logic knowledge base (KB) that encodes these premises BAT=0 O =…

A: F1 : B ^ T =&gt; O  ≈ ~(B ^ T) v O                            ≈ ~B v ~T v O F2 : O =&gt; B ≈ ~O v B…

Q: ydx -( x+***ty? dy = 0

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Q: integral F. dÃ. Compute each flux (a) F(x,y, z) = (2, 3, –5) and S is a disk of radius 1 in the…

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Q: b) Find the general and definite solutions of the first order differential equations (i) dy/dt +…

A: Solution of first order linear differential equation

Q: 5. (8³z/ôx³)2 - (5²z/ây?)5 - 15ôz/ôt (50²z/ôy?)5 - 15ôz/ôt = 0 %3D

A: We can solve this by using definition of ordinary Differential Equation and partial differential…

Q: a. Give the smallest extension of Q that contains all the zeros of x4 - 2x2 – 15.

A: We shall answer first question only as you have asked diff question without mentioning. For others…

Q: 4. If f(x) = -2*43 find X-1

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Q: the hyperbolic plane, an equiangular triangle has an area of . Find the easure of an interior angle…

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Q: I have not yet been taught Laplace Transform by my lecturer, I believe. Isn't there another way…

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Q: rectangle ABCD has side AB on the negative x axis, and side AD on the negative y-axis. POint C is on…

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Q: series solution of differential equation NO 7

A: Here we can use the generating function for Legendre’s polynomial to prove the relation…

Q: It is the a theorem useful in bracketing method, define as Let f (x) be continuous function defined…

A: We have to determine the name of theorem of the following statement ; " Let f(x) be a continuous…

Q: Solve 3 (x? + y?) dæ + æ (x² + 3y² + 6y) dy = 0 ; when x = 1, y = 0

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Q: measure of minor arc PN = 110° T. 110° L, P

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Q: * Minimize C=5x-6y Subject To 60–8xy. a. Find x*, y*, 2*, C* b. Use bordered hessian to verify.

A: This is a problem of optimization.

Q: Solve (ay? – y° /2 +æ – /2) dæ + (2 – y/T) dy =0

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Q: iv. lim h(a) =L v. lim h(r) = vi. lim h(x) = T -00

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

Q: Find the isolated singularities for the holomorphic functions f, g, h. Determine the types and…

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Q: 1. (a.) Name the given quadric surface and give its axis. (b.) Sketch the surface. (c.) Name its…

A: The three dimensional surface is represented by the equation f(x, y, z)=0. If the graph of f(x, y,…

Q: 4. Рy/Оx? - 60у/дx - 5 %3D 0

A: 4 Given differential equation is ∂2y∂x2−6∂y∂x−5=0. We have to identify the order, degree, type of…

Q: An object weighing 1000 pounds sinks in water starting from rest. Two forces act on it, a buoyant…

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Q: Finddhe nadiy of.convergeneer ef pouer series n

A: Radius of converges of the power series exaption

Q: Let II, be the plane with Cartesian equation z=0. Let II2 be the plane with Cartesian equation x=0.…

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Q: (b) Explain how the function f(x) = log(x + 3) can be graphed by using transformation of the graph…

A: (b) Given function isfx=logx+3The graph can be transformed to y=logx by the following…