Suppose that h is differentiable and h(x + y) = h(x)h(y). Find a formula for h'(x)consisting of a single term and use it to find h(0).

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A: Note: As per the guidelines we are supposed to answer only 3 subparts question. For the remaining…

Q: 4. Show that a sublinear functional p satisfies p(0) = 0 and p(-x) ≥-p(x).

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Q: 1. Evaluate the iterated integrals a) Ans: p²sing dpdedo 97 √√3 2 2 b) ² sing dpdøde Ans: 14/3 T

A: The solution is given as

Q: n 18. Let H be a subgroup of all automorphisms of a field K. Then the fixed field d of K.

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Q: If S and T are normal linear operators satisfying ST* = T* S and TS* = S*T, show that their sum S+T…

A: I have used just definition of normal operator

Q: x√1+x² dx

A: Follow the python script.

Q: 1. Solid S is bounded by the ff. surfaces. Sketch S and label its boundaries. 2y+z+x= 4, 2y+z+x=6,…

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

Q: c) Set up the objective function. d) Suppose that in the optimal solution for this problem, a…

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Q: Find the curl of = pz²cos(p)a+zsin²(p)a₂ O None of the choices O2zsin (4)…

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Q: Example 12.5. Find the maximum value of Z = 2x + 3y subject to the constraints: x + y ≤ 30, y ≥3,0 ≤…

A: The linear function that needs to be optimized(maximize or minimize) is called the objective…

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Q: A complex number has a modulus of 3 and an argument of -π/3. Another complex number has a modulus of…

A: We have given a two complex numbers , z1 and z2 We have given modulus and arguments of both the…

Q: 8. Answer the following questions. (a) Sketch the graph of f'(x) by using the given graph of y=…

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Q: Solve differential equations 1. y - xy = 0; M(1,1). - 2. y4y² = 1; M(1,0). 3. y 4. yy ry³ = 0;…

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Q: Which of the following is true for the integral A. In 5-In(-2) B. In 5-In 2 C. -In 5 + In 2 D. In 5…

A: Sometimes, the integrand of a definite integral is undefined at any of the two limits or at a point…

Q: DIE the solution. оn If ind a) зхун 6 x2y! +12 xy=ex+о I the value

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: 4 Which of the following is true for the integral A. In 5-In(-2) B. In 5-In 2 C. -In 5 + In 2 D. In…

A: Solution no. (2)  Options (B) is correct

Q: Give an example of a differentiable function g: R→ R such that f is strictly increasing on R but g'…

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Q: 3. Let R be the region lying outside r = 1 and inside r = 1 + cos 0. (i) Sketch the graph of the…

A: The area that is enclosed by a polar curve represented by r=fθ with θ∈a,b is formulated by the…

Q: Z = (1 - j)¹-2j

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Q: 2. Let AM₁ (R) be given. (a) If AA=0, prove that A-0₁. Does this hold if A € M₁(C)? (b) Suppose that…

A: This is the problem of Linear Algebra and Linear Transformation.

Q: acid, HO₂C H, the first ionizatio Ka₂=4.2. Why is the second carboxyl g

A: Acids will sour substances with the pH values less than 7. Acids can donate their protons. There are…

Q: > Fill in the missing steps to determine convergence or divergence of the following series (4) + n-1…

A: Given series is ,…

Q: Find the Inverse Laplace Transform of 10. F (s) 2s+3 s²+4s+13

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Q: Prove that span (v1,v2,...,vn) is a valid subspace of R

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Q: What is the value of y in (2x - 1) + j(x + y) = (y - 6) + j(2y - 4)? Rectangular form answer please

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Q: ▪ Solve the following SLEs in a clean sheet of paper (preferably bond paper). ▪ Show a complete,…

A: Solution

Q: Differential equation of a family of curves. In each of the following problems, obtain the…

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

Q: A Norman window is in the shape of a rectangle surmounted by a semi-circle.

A: We have to solve given problems:

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Q: Prove that the intersection line of the planes P₁: 2x -y - 2z = 0 and P₂:x-2y+z = 0 is parallel to…

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: Use Simpson's Rule to evaluate the following. n = 10 3 1 dx -3 1+x²

A: Simpson's 13 rule: ∫abydx=h3(y0+4(y1+y3+y5+...++yn-1)+2(y2+y4+y6+...+yn-2)+yn), where h=b-aN and N…

Q: 1.1 2. t 3. e3t 4. t sin 3t 5. et sin 3t

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Q: Example 10.11. Using modified Euler's method, find y(0.2) and y(0.4) given y = y + e*, y(0) = 0.

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Q: Let x, y € R" be given. (a) If ||z||||y||=1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1 and ||y||…

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Q: Let S be the solid of integration of the given integral Q. (1.) Sketch S and label its boundaries.…

A: From limit of given integral we will find the region bounded and then draw the diagram . While…

Q: y = 4(1-x²), y =1-x² 5. y=

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Q: d) Given a and r = -5, calculate S6. 2 e) Given tn = 3tn-1+2 and t4 = (-2), find ts.

A: Solution

Q: Find and explain an example of a Riemann Integrable function that does no have an antiderivative.

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Q: A 25 C 75 3 ull₂ = 8,ab= 25 then (a + b)2²= B 100 D 50

A: The solution is given as

Q: Solve the following differential equations: 1. () + (x −2x*)y'+xx=0

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Q: | Example 11.4. Solve the Laplace equation ux + y = 0 given that xx 0 11.1 17 19.7 18.6 0 21.9 0 21…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)²=2y, the…

A: Follow the steps.

Q: Using the power series method about x = 0, the recurrence relation of the differential equation: y"…

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Q: Set up the iterated triple integral that will give the following: (please provide a clearer and…

A: In general, volume integrals are triple integral, which involves the integral with respect to x,y,…

Q: Consider the sequence of functions {f} defined on the interval [0, 1], where fn(r)= nx 1+n²r²¹ Vx €…

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Q: There are three numbers in geometric progression whose sum is 26. If the first is increased by 2,…

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Q: 1. Let 1, y € R" be given. (a) If ||z|| = ||y|| = 1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1…

A: \documentclass{article}\usepackage{amsmath,amssymb}\begin{document} (a) Norm x=Norm y=1\\ Let angle…

Q: Consider the equation du 2y = 0, y(0) = a. Let I = (-1, 1). Which statement below is NOT true? (A)…

A: First we can solve using separable method