Prove or give a counter-example:

Q: 1. Evaluate x+√√x for x=-5:0.1:5:

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Q: If f(x) dx = -2 and g(y) dy = 4, what is the value of ff f(x)g(y)dA where (D: 1 ≤x≤ 3,-5 ≤ y ≤-4}

A: Given ,     ∫13f(x) dx = -2   ,     ∫-5-4g(y)dy = 4 Then the value of   ∫∫D f(x) g(y) dA  , where…

Q: Let the vectors (i, j, k) constitute an orthonormal basis. In terms of this basis, a general basis…

A: Dual basis: Given a basis β={e1,...,en}, its dual is β*={e1,...,en} such that ei(ej)=δij. where…

Q: ..HW... solve the following equat.1.9.4.2.......... -2x+y=1" ....... *****

A: Here we have to solve the given differential equation.

Q: Which of the following is the field that is aimed at the construction error-correcting codes? O…

A: This is a problem of coding theory.

Q: 2. Given vectors A= i + 2j + 3k, B= 2i + j - 5k Determines: 3.The vector component of vector A…

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Q: Exercise 13.4.22. (a) In the group D₁, let r be counterclockwise rotation by 2π/n and let s be the…

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Q: You may round answers to 2 decimal places if desired. Maximize f = 3x + 6y + 10z subject to 2x + 5y…

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Q: Interpret 4xy² lim (x,y)-(0,0) x²+3y4 along x

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Q: 2. Let ƒ : R² → R where f(x, y) = x²y, c = (1, 2), and u = (1,0). Use the E-6 definition to prove L₂…

A: Given: f: ℝ2→ℝ,  f(x,y)=x2y,     c=(1,2),    u(1,0)

Q: Problem 5.7 Minimize the functional J(r()) = (s)-1]²[* (s) + 1]² ds, [* 0 subject to the endpoint…

A: Use alternate form of euler lagrange to obtain solution as  x=s2as minimizing curve.

Q: Given the following integral and value of n, approximate the following integral using the methods…

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Q: (3) Find the general solution of d = t³y. Check for yourself if you got the correct family by…

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Q: x-2y Which method would you use to evaluate the limit lim (x,y) → (2.1) 4y-x² 3 and what conclusion…

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Q: A thermometer is removed from a room where the temperature is 70° F and is taken outside, where the…

A: The Newtons law of cooling is defined by dTdt=kT-Tm where k is the constant of proportionality. Here…

Q: Find 2 by 2 symmetric matrices S = ST with these properties:(a) Sis not invertible.(b) S is…

A: Given: Let S be a 2×2 symmetric matrix. To Find : a) S is not invertible. b) S is invertible but…

Q: 8. Find the square roots of 1-√3i and express in rectangular coordinates. 9. Write the function f…

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

Q: How much longer should you expect Gaussian elimination to work on a system of 1000 equations versus…

A: Number of multiplications required by a system of equations of n equations is given by the equation;…

Q: (Describe the steps of the proof carefully so that the Problem 5. Short Proof logic you follow is…

A: It is given that, a1 and a2 be two linearly independent vectors in ℝ5. And, B be the 3×5 matrix…

Q: Check all the properties of the logistics DDS that are true: 1) The logistics DDS is more realistic…

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Q: 2. a. Use the inversion algorithm to find the inverse of the matrix, if the inverse exists. 1 1 1 0…

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Q: Let the vectors (i, j, k) constitute an orthonormal basis. In terms of this basis, a general basis…

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Q: Find a counterexample to show that the statement is false. (Select all that apply.) 1 X x>- Ox>2…

A: Given x>1x. This can be written as: x>1x⇒x2>1 Consider the equality x2=1. Solving this:…

Q: Graph y=-x+5 on the grid below. Then, graph y=-x+5 on the same grid. 4 a) Write the coordinates of…

A: For a function: y=f(x), the set of real values of x for which f(x) is defined is called the domain…

Q: 3. Let f: R2 → R2 where f(x, y) = (x²y, 3x + 2y), c = (1,1), and u = (1, 1). Use the e-d definition…

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Q: Compute the following: (your answer should be the least nonnegative solution). Show reasoning (i) 87…

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Q: Suppose ƒ : (0, 1) → R is uniformly continuous. (i) Prove that f is bounded. (ii) Prove that limx→0+…

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Q: ((x + 1)5 + 3y)dx − (x + 1)dy = 0 -

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Q: Sketch a cycle of the graph of each of the functions defined below and then indicates the…

A: For a function: y=f(x), the set of real values of x for which f(x) is defined is called the domain…

Q: Define T: P3 R¹ by T(p)= p(-3)] P(-1) p(1) p(3) where P3 = {a+at+a₂t²+₂t³ | α α₁₁ a₂. a are reals }…

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Q: In R=Z_24, partition this ring into its zero, zero divisors and units. (Draw the partition on your…

A: We know, in a non-trivial ring R with unity an element a in R is said to be a unit if there exists…

Q: 3. The principal normal vector field is defined by : (a) T¹ (s) (b) r(t) |r' (t) (c) |T'(s)| |T'(s)|…

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Q: Two chemicals A and B are combined to form a chemical C. The rate of the reaction is proportional to…

A: Given: Two chemical A and B are combined to form a chemical C. The rate is proportional to…

Q: Let f be the function whose graph is shown below. -3 -2 -1 y 2 + 0 1 2 3 4 5 x Estimate the two…

A: Let  a function f:a,b→ℝ be such that  (i) f is continuous on a,b and  (ii) f is differentiable at…

Q: Let lim f(x)= 36. Use the limit rules to find the following limit X-2 lim √f(x) X-2 lim √√f(x) = X-2…

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Q: QUESTION 17 Find (1) (ii) F(x,y) dy F(x,y) ds where F(x, y) = 1 and C is the curve y=x²-Inx from…

A: Given that Fx,y=1 and C: y=12x2-14lnx from 1,12 to 2, 2-14ln2.

Q: Find (1) (ii) F(x,y) dy F(x, y) ds where F(x, y) = 1 and C is the curve y=x²-Inx from (1,2) to (2,2…

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Q: 2 Locate the numbers z₁+z₂ and z, - z₂ vectorially when z₁ = 2i, z₂ ==-i. 3

A: Use addition the evaluate these numbers then plot it

Q: Solve the following Initial Value Problem: ex e2x + 1 y': = y, y = y(x),y(0) = 1

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Q: Thirty-five cities were researched to determine whether they had a professional sports team, a…

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Q: 3. Let T(-) be a linear transformation such that T(a) = 0 for a 0 and let c be a vector such T(c)=d,…

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Q: (b) (3 points) (*) Find a critical point of g(x, y) and determine whether it is a local maximum, a…

A: Given : gx , y=x2+y29. To find : critical point of gx,y. To check : gx,y is local maximum , local…

Q: For each problem, find the x-coordinates of all points of inflection, find all discontinuities, and…

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Q: Prove the statement using the , & definition of a limit. lim x2 = 0 x-0 Given & > 0, we need &…

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Q: Find the maximum rate of increase of f at (-2,1), and the direction in which this occurs.

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Q: X = 25° 50° xº

A: Consider the circle below. Using the Angle of Intersecting Secants Theorem, it can be written that:…

Q: Let E be an extension field of the field F. Show that the automorphismgroup of E fixing F is indeed…

A: It is given that, E be an extension field of the field F. We have to show that, the automorphism…

Q: Show that exp(z²)| ≤ exp(|z|²) for all - E C.

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Q: Use the given graph of f(x) = √x to find a number & such that if |x - 4| < & then √x - 2 <0.4. 8 = y…

A: Given Data: Let us consider the given graph, fx = x if x-4 &lt;δ then x-2&lt;0.4

Q: Exercise 4 Prove that the following differential equation x-1 (y − 1)²dx + (xy-2x+² |dy = 0, y =…

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