Prove that the following function is continuous at 0. x, if x is rational f(x) = {0, if 0, if x is irrational

Q: Work all your computations at an accuracy of 3 digits after the decimal point. Stop the iterations…

A: Given: fx=4ex+16x0.3-40 and x0=2.43 εa=xi-xi-1xi×100% Using the fixed-point iteration method we have…

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Q: Question 2 of 6 Let X and Y be random variables with E(Y) = 5, Var(Y) = 6, E(X) = 3, Var(X) = 4, and…

A: Let X and Y be random variables with E(Y) = 5, Var(Y) = 6, E(X) = 3, Var(X) = 4, and Cov(X, Y) = 0.…

Q: Use the separation of variables method to solve Ut = 3uct, 0 0 u(0,t) = u(1,t) = 0 u(x,0) = –2…

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Q: Question 1. State whether True or False. Provide a reason in each case. a. The pair (No, +)…

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Q: PART 2. PROBLEM SOLVING. Show all necessary computations and provide a sketch of the region of…

A: PART 2. ------Question (1)----------SOLUTION:-

Q: Q1/ Solve the equation: 4fxx(x,t)=ft(x,t) f(x, 0)=20(6-x) f(0,t)=0 f(6,t)=0 Take h=1 for 0< t <2 and…

A: We suppose, ux,t=XxTt So, utx,t=XxT'tuxx,t=X'xTtuxxx,t=X''xTt So, from the given partial…

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Q: (d) Show that the polynomials P₁ = 3 + 2x + x², P₂ = 2x+3x², p3= −2+x=2x² form a basis of the vector…

A: Using 1+2x-x^2=ap1+bp2+cp3 find a b c

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Q: 7. Express 55C14 + 54C14 +54C15 as a single term from Pascal's triangle.

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Q: 3. Show that the differential equation zxy

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Q: 2. Using the Laplace transform find the solution for the following equatic a y(t) = e(-31) With the…

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Q: Suppose that 0.3210 approximates 0.3245. How many significant digits does the approximate have? O 3…

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Q: Suppose that an is defined by setting a = = -2, a₂ = 0, and an = 4an-1-4an-29 where n ≥ 3. Using…

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

Q: 5. Find the conjugacy classes in D4 and write down the class equation forD4. (To get full credit for…

A: 5. Given is the table of D4.   To Find: The conjugacy classes of D4 and write down the class…

Q: (a) Let f: R¹ → R, f(x, y, z, w) = +2y² +8z²+3w³ + xy + z-w. i. Calculate the Hessian Matrix for f.…

A: Given: f:ℝ4→ℝ, fx,y,z,w=x22+2y2+8z2+3w3+xy+z-w We have to find: (i) Hessian matrix for f. (ii)…

Q: If L, CL₂ and L₂ CL4, then L₁ L3 C L₂ L4 Select one: O True O False

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Q: x1 + x2 + x3 2x1 + 3x2 + 4x3 3x1 +4x2+2x3 6 20 = 17. = =

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Q: Find all values of the full power. ASAP 2 (ei)√₂

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Q: let 4 be a Hilbert space and s, and so be any two subset of H then (3) {o? ² = H (") SAS+ = {0} 9,…

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Q: Find the edge chromatic number of Kₙ when n is a positive integer.

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Q: 1. Consider the ollowing linear system, E 2x₁ + x₂x3 + 2x4 4x1 + 5x2 − 3x3 + 6x4 -2x1 + 5x2 - 2x3 +…

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Q: Find the area of the region bounded by the curves y = e* y² = 4x - 4 between y = 1 and y = 2. and

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Q: The owner of a mid-size company advertises on the television and on the radio. He has found that the…

A: We need to determine the value of x, y such that the function: N(x, y)=-0.5x2-0.9y2+13x+18y+350 is…

Q: 5. (cont.) Using f(x) = x ln √√x + 2x ; Do each of the following: C. Perform the 1st derivative test…

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Q: Let p be an odd prime number. Prove that [(3)=1] → [p = 1 mod 6).

A: Introduction: A positive integer that is the area of a right triangle with three rational number…

Q: Find all values of the full power. ASAP 2 (ei)√₂

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Q: Consider the function f(x, y) = ax - 2y + 1 where a is a positive number. S SR ax 2y + 1 dA 45,…

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Q: - theorm; – Every inner product space is a norm linear space

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Q: Given that P (10, 12), Q = (10.3, 12.1), f(P) = 50 and f(Q) = 57, = : approximate the directional…

A: Given that P=10, 12,   Q=10.3, 12.1,   fP=50,    fQ=57   To Approximate: The directional derivative…

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Q: 2611 Use the Max-Min Inequality to find upper and lower bounds for and 0.5 S d 1+x² Add these to…

A: Given That : ∫0.511+x2dx and ∫.5111+x2dx To find : upper and lower bound using the Max-Min…

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Q: Let T: R3 → R3 be a linear trans formation such that T(1,1,1)=(2,0,-1),T(0,-1,2) = (-3,2,-1) and…

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Q: section (measuring x inches to a side) and costing $100 to ship, the function V(x) = x²(400 – 4x)…

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Q: All eigenvalues of a Regular Sturm-Liouville problem are strictly positive. Eigenfunctions of a…

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Q: (a) Find the critical numbers of the function f(x) = x(x - 2)5. X= (smallest value) x= (largest…

A: a) Find the critical numbers of the function fx=x6x-25.   b) Tell about the behavior of f at these…