(30) Prove the following inequalities: log x 1 (a) Vr € R \{1}, X - 1 - √x (b) Vn € N, e- e − ( 1 + ¹ )" < - e 2n + 1 n

Q: (c) Calculate dx √x(x+1)

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Q: blem 5. Let P, be the vector space of all polynomials of degree 2 or less, and let H be the subspace…

A: Find the dimension of the subspace we need to determine the number of independent vectors given in…

Q: 6: The function f(x) = x + x² - 16x₁ - 4x₂ has minimizers points at A: [] and [2] B: [2] and [4] C:…

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Q: x=3 Qs. A: Find * x²dx by using Riemann integral.

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: If mx = 1 (mod n) has a solution, then nx = 1 (mod m) has no a solution. Select one: True False

A: We know the definition of Congruence ,  Suppose m be a positive integer , we say that integers a and…

Q: Find r'(t). cos 4 cos³(t)i + 2 sin³ (t)j + k r(t) = 4

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Q: 5:2 Find the 2-transform of the sequence x(n)=-duc-m-1) and draw Zero - pole diagram with…

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Q: L-1 S s-1 (s² +9) Find laplace inverse

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Q: 6. Evaluate the inverse z-transform of x(z)= 2z-1 (1-2z-1)2

A: Given: xz=2z-11-2z-12 To find: Inverse z-transform of given function.

Q: * 2: The function f(x) = x² + 2x² + 3x² + 4x₁x₂ + 5x₂x3 + 6x1x3 can be written in the form f(X) =…

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Q: x1 + x2 + x3 = 0 x4+x₂+2x3 = 0

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Q: If = (1,0), then Düfz(-3,4)= ƒxy(−3, 4). True False

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Q: The multiplicative inverse of x²+x-1 in Z5 [x]/ is: O x^3 O x+1 O x^4 O None

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Q: (c) Explain the Bisection Method to compute a real root of f(x) = 0 and find the condition of…

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Q: Solve the following boundary value problem for the Laplace equation using the method of separation…

A: Let uxx+uyy=0   ……………………………(1)u(0,y)=u(x,b)=0 ,  u(a,y)=u(x,0)=1 Let the solution of equation(1) by…

Q: Find the orthogonal projection of -10 14 11 V = 15 onto the subspace V of R4 spanned by -1 2 1 X1 =…

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Q: Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli…

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

Q: Evaluate the definite integral. L₁(8+ 8ti +8t³j + √√tk) dt

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Q: Problem 3 (A) Solve the matrix equation Ax-b where A- (B) Is it possible to solve Ax b for any given…

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Q: Consider two brine tanks connected as shown in the figure below. Tank 1 contains x(t) pounds of salt…

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Q: By using the unlimited coefficients method, choose the correct answer for this equation y"-y'-2y=0…

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Q: find serious solution of differential equation (x+3)^2y''-9(x+3)y'+25y=0

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Q: 1. Determine whether the differential equation d²y dy dx² dx has the solution y xe22 = 28 2x e²x +…

A: Introduction:   A differential equation is an equation that contains the derivative of an unknown…

Q: H.w 3: Apply the Trapezoidal rule to evaluate SiSit 2xydxdy (1+x²)(1+y²)' taking h = k = 0.25. 110 +…

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Q: Consider the differential equation dy (yt)¹/5 (y>0, t≥ 0) = dt (a) State the form of the…

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Q: Construct a right angled triangle having the longest side 84 mm and one angle 38°. Measure the other…

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Q: (a) For each of the following linear transformations, write down its matrix and describe its type.…

A: (a) To find: the transformation matrices. Please post the multiple questions separately. Here I…

Q: Hand written plz 2. Standardize the following LP model. max z = −3x₁ + 8x₂ − x3 + 12x4 - - - 3x₁…

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Q: Question: iz -iz (a) Let f(z) = e + e 2 Go show that f is periodic with real period 2Ã

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: In this problem you will solve the nonhomogeneous system ✓ = [_3__3] + [3] y' -9 -3 A. Write a…

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Q: Borderland and are now asked by the game m Arisu must decide between the light and dar el and demon…

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Q: 1 Obtain a numerical solution of y-1 = using Euler's method with step size equal to (0.02) y and…

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Q: -labelled diagram and calculate the Fill in the blanks below after you ha

A: Given the air speed of the plane is 655 km/h at a bearing of 15°.  The wind speed is 45 km/h at a…

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A: We use definition of Z-Transform.

Q: Find the measure of the arc or angle

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Q: 3 Factorise completely the expression 2x³-11x²-20x-7.

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Q: Applications of Integral Calculus Suppose the shaded region below is revolved about the y-axis.…

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Q: Use synthetic division to divide. (Simplify your answer completely.) x5-13x4 120x + 81 x + 3 X = -3…

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Q: Let A be a matrix with only two eigenvalues. It is known that: λ = 2-i has two vectors 1 and 2-i…

A: Result: If a matrix has eigenvectors corresponding to a particular eigenvalue, then its linear…

Q: 3 -6 -1 -4 -3 4 et y = ,V1= " 5 -1 Compute the distance d from y to the subspace of R4 panned by v₁…

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Q: Decide which of the matrices can be squared and calculate the squares. Calculate (if possible) A-¹…

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Q: Check whether these statement are consistent or not: a. ¬(p Vq) and (pq) b. rqAr and ¬(qV¬r)

A: Introduction: Two propositions are referred to as consistent when their truth values are same at…

Q: 2. Given the following data: X -20 12 4 f(x) -11 1 -2 5 97 Newton divided difference polynomial…

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Q: 5. Evaluate the following integral [² 2x cos² x dx by using Trapezoidal's rule with 6 subintervals.…

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Q: . Use x,  y and z as variables to rewrite the following sentences to mathematical statements  A…

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Q: O Consider the following matrices 0 ^- (-¹2 ~) -- († ;) -- (1 ¹/² : ;) -- (:) --( : ) 1/2 3 A = D= 1…

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Q: 10. Using 5x5 grids, determine the equation for steady state temperature distribution at T21, T22…

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Q: Max (Z) = 3 X + 5Y Constraints: 2X +3Y≤ 30 5X +4Y≤60 By Condition X, Y20

A: Given LPP is max z=3x+5ysubject to2x+3y≤305x+4y≤60x,y≥0   So, graph of  function

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A: A function is homeomorphic when it follows the bijection. The bijective property is one of the…

Q: H.w1: evaluate fe* siny dx dy i) using the trapizodial rule in both direction, Ax= Ay = 0.1 ii)…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…