1. (4 points) Show that the space (C([a, b]), ||· ||∞) is a Banach space.

Q: h b The figure shows the cross section of a channel carrying water. Determine h, b and that minimize…

A: Given: The cross-section of a channel carrying water.To find: h, b, θ

Q: X |_ [² é

A: Given differential equation x'=x+2y-6e-ty'=4x+y-8e-t From the homogeneous solution given it is clear…

Q: 2. Let C be the semicircle z = 2e where 0 ≤ 0 ≤ T. Show that < C -dz ≤ z² +1 2π√/2 3

A: Given: z=2eiθ , 0≤θ≤π To show: ∫Czz2+1≤2π23

Q: 2. (6 marks) Find the vector equation of a plane a) Passing through the point A(-1, 2, -3) and…

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Q: Consider the group GL₂(R). Let A (a) Find all elements of H = (A). (b) What is A|? √2 2 √2 2 NANS √2

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Q: Show that the following relation is not a function on R {(x, y) ∈ R × R : x = cos(y)}

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Q: 6.) [D³ + 6D² + 11D +6] (yx) = 0 7.) [4D³ + 4D² +D](ro) = 0 8.) [D¹ + 2D³ + 10D²](yx) = 0

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Q: A large pizza cost $2.50 more than a small one. Five large and two small cost $73.75. Find the cost…

A: Let assume large pizza cost is = L small pizza cost is = s According to question A large pizza cost$…

Q: A variable plane pes through a fixed point (a, b, c) and meets the uses at A, B and C. Show that the…

A: Given that a variable plane passes through a fixed point (a, b, c) and meets the uses at A, B, and…

Q: y=x−x+e*(x+cosx)

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Q: A 10-year annuity makes continuous payments. At time tt, the annuity pays at an annual rate of…

A: f(t) = 30 - 3t Therefore the integral is given by: ∫010(30-3t) e-0.05t dt = -3∫010(t-10) e-t20 dt…

Q: A bag of candy contains red, yellow, green, and blue candies. The odds of randomly picking out a…

A: The odds of randomly picking out a candy that is blue is 3:12

Q: 100 8. Rewrite log2 II* П 24 as an expression involving summation notation. i=10

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Q: ест Cramer's rule to save the system of X₁ + x₂ + 2x3 - xy = 1 1 X₁-2x₂-x3 + 2xy = 0 x₁2x2 + x3 + xy…

A: Given system of linear equations can be written as  112-11-2-121-21106-24x1x2x3x4=1020 which is of…

Q: Let A be a nonsingular 2 × 2 matrix with singularvalue decomposition A = USVT and singular valuess1…

A: Given That :  A be a nonsingular 2×2 matrix with singular value decomposition A=USVT and singular…

Q: d²V = f(x) 0<x<L dx² = f(x) V(x = 0) = V₁ V(x = L) = V₂

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Q: State the first minimum and maximum point to the right of the y- axis of the given function: y = 5…

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Q: y = e-³x cos3x

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Q: Identify the range and the x-value(s) of the visible vertical asymptote(s): -21 नं -L EN O -K/N NET…

A: A graph of a function is given. Our aim is to find the range and vertical asymptotes of the graph.

Q: Transformation of Ax for: A = [3   1                              x = [2       2    -4]…

A: We have  A=312-4, x=21 Transformation  Tx=Ax

Q: Determine whether the series 3⋅1!/1+32⋅2!/22+33⋅3!/33+…+3n⋅n!/nn+… converges or diverges.

A: Given series is 3·1·1!/1+3·2·2!/2·2+3·3·3!/3·3+…+3·n·n!/n·n To Determine : Whether the above series…

Q: 5- Is the following a one to one function when defined from all reals to all reals? y = √x Give a…

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Q: Example 6.24. Using Mil dy (t dt equation For y(2), given that (0) 2

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Q: Given the angle 31 12 0 state all co-terminal angles to theta, in the interval -2t < 0 < 3t 0: ㅠ =…

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Q: Given the point P(-√√√42) on the unit circle, state the values of a) - b) -√√ 1/1/1 c) √42 7 O to d)…

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Q: Q3-B: Verify the Kummer transformation: U(a,c;x) = x¹-U(a-c+1,2-c;x)

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Q: Given the radius of a circle r = 4 cm and the central angle = Calculate the arc length (a) and…

A: The answer provided below has been developed in a clear step by step manner.

Q: Using Lyapunov's method to dtermine the st. for the following systems. dx dt dy dt -2y - x5, 3x -…

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Q: 10. Consider the function: f(r) = ¹-. Find all maxima, minima and points of inflection for this…

A: Given: f(x)=x4-x6To find: Maxima, minima, and inflection points.              The plot of the…

Q: find the sum of 1X ¹x (2-6) X (2-60²) + 2X (3 - w) x ( 2² w²) + -+ (-1x (m-w) x (m-1²);

A: A

Q: x=t(e²¹

A: We have x=te2t+4

Q: = 3 2 +fe² 0 ₂+² + e+tu(t)dt

A: As per the question we are given an Fredholm type integral equation which we have to solve using the…

Q: Let C be the circle |z −1| < 2 taken in the positive sense.

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Q: which are Subspaces of RB & find abasă to those that <x+y, x+z, g+z)..... < x, y, z) 936

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Q: arithmetic progression a,

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Q: Beni franvere axis of hypebola is 5 Tangent at point p and normal to this tagent meet conjugate axis…

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Q: Area of a region in a plane Let R be a region in a plane that (a, b, c) and boundary C. Let has a…

A: Given That : Let R be a region in the plane that has a unit normal vector n=a , b , c and F=bz , cx…

Q: 1.) [D³ + 6D² + 11D +6] (y₂) = 0 2.) [4D³ + 4D²+D](re) = 0 3.) [D5 − 5D² + 7D³ + D² − 8D + 4](x₂) =…

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Q: Let C be the circle |z −1| < 2 taken in the positive sense. Evaluate the integral below

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Q: A periodic function is defined by f(x + p) = f(x), where p is the period of f(x). Assume a periodic…

A: note : Since you have posted multiple questions with multiple sub parts, we will provide the…

Q: Solve the problem. For what values of t is r(t) = cos t i + sin t j + sqrt( 9- t2) k continuous?

A: A vector-valued function r(t) is continuous at t=a if and only if: 1. r(a) is defined. 2. limt→ar(a)…

Q: 5. Let P2(C) be the vector space of polynomials of degree less than or equal to 2 over C. Let C3 be…

A: 5) Let P2ℂ be the vector space of all polynomials of degree less than or equal to 2 over ℂ. and ℂ3…

Q: What's wrong? Consider the rotation field F (-y, x) x² + y? * a. Verify that the two-dimensional…

A: The given vector field is, F=-y,xx2+y2. (a) To Show: Two-dimensional curl of F is 0 and double…

Q: 6. Use the following form graph of yos-2 is the below 162 que lo miog snil letnosion of 20 (anato…

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Q: 2- Fill in the multiplication table and the addition table z₂ = {0,1}

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Q: The series converges for every x in the half-open interval [−1, 1) but does not convergewhen x = 1.…

A: Given: The series converges fx=∑n=1∞xnn=x+x22+x33+x44+.... for every x in the half-open interval…

Q: Which of the following represents the answers of all vertical asymptotes beyond the given graph…

A: We will use concept of vertical asymptotes to find points

Q: 2. Let o (1,2,3) (2,3,4,5). = (a) Write σ as a multiplication (b) Write o as a multiplication (c)…

A: The given permutation σ=1232345. We have to write σ as a disjoint cycle, multiplication of…

Q: d 3. Find the herrel of the linear transformati L: R³ R³ with matrix 2 5 1 390 1 4 -1

A: To find kernel, we have to find null space of corresponding matrix.

Q: v=x²e=x + 4e²

A: Given solutiony=x2e-x+4ex