CONTINUITY AND DISCONTINUITY OF FUNCTIONS Instructions: Answer this set together with your groupmates. Show all pertinent solutions/workings, when required, and box final answers. Every item without supporting solutions will merit a score of zero even if the final answer is correct. For each item, do the following: a. Find the possible points of discontinuity (PPD) of f b. Discuss the continuity of f at the PPD. Redefine the function in case of removable discontinuity. sin² 2x , if x < 0 2x2 2. g(x) = {2 12х — 3 if 0

Q: Ql: Find out whether each of the following functions is a solution of the ODE. (choose 1) p(x) - 5p"…

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Q: (a) Let * be defined on Z by a * b = 2ab. Determine whether the binary operator defined is…

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Q: 1. Using LU decomposition Cholesky 4x1 + 10x2 + 8x3 = 44 10x1 + 26x2 + 26x3 = 128 8x1 + 26x2 + 61x3…

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Q: ) Let T : R? → R? be a linear transformation that sends the vector u = (5,2) into (2, 1) and maps i…

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Q: 3) Find 25 x 0.25 A) 0.625 B) 6.25 9 62.5 D) 625 4) Simplify by combining like terms: 3x + 3x + 3x…

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Q: Solve the recurrence relation an = 7an-1 – 10am-2; ao = 2, a1 = 3 %3D O 4, = }5" – 2" 2" – 5" An = -…

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Q: 1. Let the function C = f(n) represent the total cost C (in dollars) for a carpenter when building n…

A: Introduction: A mapping or function whose domain and codomain are subsets of the set of real numbers…

Q: Discrete math: Let P(n) be the statement n! < nⁿ , where n is an integer greater than 1. Use…

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Q: How much should you invest now at 5% compounded quarterly to have $8000 in 4 years?

A: As in compound interest quarterly A = P1+rnnt

Q: Find the radius of convergence of Power Series fca) = E 1ogn. z"

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Q: Question 7: The dimensions of a rectangle are represented by rational expressions, as shown in the…

A: Here the given rectangle is                                          Here the height is 6x+2 and…

Q: 1-Determine if W is a subspace of Mnn CEMn,W = {AEMnn: CA'C1= A}

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Q: 2 11 -10 -9 -8 -7 -6 -5 /-4 -3 -2 -1 2 3 4 5/6 7 8 9 -2 The curve above is the graph of a sinusoidal…

A: Find the sinusoidal equation of the given graph. The general equation for the sinusoidal function is…

Q: ---A 2 Let aj 1 and ag -10 The set {a1, az, ag} will span R unless h

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Q: ompute the gcd of 11 + i and 61 in Z[i] to find x + yi such that x2 + y? = 61.

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Q: a. What is the center of this series? b.  Find the radius of convergence of the series.  c. Find…

A: Introduction: The infinite power series in the variable x centered at x=a is fx=∑n=0∞cnx-an Here, cn…

Q: what is the final answer

A: The final answer is dwdt=8t−14t2−t+4

Q: Find a power-series solution for the following differential equation d'y dy +*+x*y 0 dx dx You may…

A: We find a power series solution of the given differential equation  y"+xy'+x2y=0.......(1)

Q: Find a singular value decomposition UEVT for A = 1

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Q: Find the radius of convergence and interval of convergence of the power series. 13. 2 n=0 n!

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Q: 6. Find and classify all the equilibrium solutions of the given differential equation dy (y? – 4)(y…

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Q: 1. The integral of J, \z|dz along any closed path y is 0.

A: As per our guidelines, we suppose to answer only one question in case of multiple questions posted.…

Q: Let a, be recursively defined by ao = 3, an+1 = a - an for n 2 0. Find lim an.

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Q: 2^2013 -2^2014 × 2

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Q: 1. Represent each of the following sequences by a formula, a, = f (n), with the given starting…

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Q: 3- Let {u,v,w} be a basis for a vector space V. Is {u + v,u + w,v + w} a basis for V?

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Q: Let A CX with the discrete topology. Prove that ô(A) = Ø.

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Q: (a) L{t + sin 4t – e2t cosh rt} (b) L{e' + cos 4t U(t – 1/2)} - (c) L-!{ s + 1 (s +2)(s² + 2s + 5)…

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Q: (a) Illustrate in the complex plane those complex numbers z =1+ iy E C for which m (s + ) >. Im (z+

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Q: (e) Let S be the set of all real numbers except-1. Define * on S by a * b = a +b+ ab. Show that if *…

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Q: For which positive integers k is the following series convergent? 8. (kn)! n = 1 k ? 0

A: Series and sequences, ratio test

Q: Write x as the sum of two vectors, one in Span (u,,u2.u3} and one in Span fu,}. Assume that {u, .ug}…

A: To find- Write x as the sum of two vectors, one in Span u1, u2, u3, and one in Span u4. Assume that…

Q: Evaluate the sum. 30 j=1

A: We have to find the sum of the series

Q: A student borrows ​$1000 at 15​% for 6 months to pay tuition. Find the total amount due using simple…

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Q: 1. Let S be the set of all 2 x 2 matrices of the form with respect to matrix addition and…

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Q: 2-Show that the following polynomials from a basis for P2. 1- 3x + 2x2,1 + x + 4x²,1 – 7x

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Q: Suppose that an amount of 10,000 dollars is invested at an annual interest rate of r% compounded…

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Q: Consider the differential equation f(8) – 6 f(2) + 11f(1) – 6f = 0 We transform this differential…

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Q: 1. Evaluate the line integrals x + Y ds and

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

Q: 7) What is the result of adding 35 to -35? A) -70 B) 0 C) 35 D) 70

A: 35 + (-35) = ?

Q: Exercise 3: Solve the heat equation on the square [0, 7] × [0, 71] subject to the following bound-…

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Q: A condominium unit is being amortized with a quarterly payment of P56,000 for 5 years at 3%…

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Q: mine the equation of the tangent to the circle (x+4)² +(y+2)² = 50 at the poi (1; 3) (2) (-9; 3)

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Q: For the following quadratic forms (i) write down the symmetric matrix A (so the form is equal to…

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Q: Find the radius of convergence of Power Series fca) = E n'agn. z"

A: The given problem is to find the radius of convergence of the given complex power series. We can use…

Q: Using mathematical induction, prove that 3ⁿ < n! if n is an integer greater than 6.

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Q: 1. Solve the following DE using TWO DIFFERENT methods (Two dif- ferent approaches to same method…

A: Introduction: The separation of variables is a method for solving ordinary and partial differential…

Q: Factor 11 + 3i in Z[i] into indecomposable Gaussian integers. Hint: use the norm to guess factors.

A: Using the norm to guess the factors.

Q: Find all the eigenvalues (real and complex) of the matrix -10 -8 -4 M = 10 1 18 11 7 The eigenvalues…

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Q: The dot product of two vectors in R3 is defined by = a¡b1 + azb2 + azb3. [b3] a2 b2 8 Let i Find the…

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