AP1) Prove that f: E → R; x x² is uniformly continuous if E is bounded. AP2) Prove that f : R R; x x is not uniformly continuous.

Q: Write the volume of the region bounded by z = 8- 22-y? and z = a? + y? as a TRIPLE integral in the…

A: We have to write the volume of the region bounded by z=8−x2−y2 and z=x2+y2 as a triple integral in…

Q: Us an first raflects O Find the trans-formation that vectors thorough the x-axis and then' gotates…

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Q: 8. (Liouville's theorem, Cauchy estimates and the maximum modulus principle) (a) Suppose that f is…

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Q: Graph the system of equation and write its solution x+2y=2 Note that you can also answer "No…

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Q: 19. Find the distance from the point (2, -1,-4) to the line through the points (3, -2, 2) and…

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Q: Use the graph of the polynomial function f(x) (a) to solve f(x)= 0, and (b) find the factorization…

A: Given, Polynomial function, f(x)=-0.5x3+2x2+2x-8 To find: a) Roots of f(x)               b)…

Q: а) Using elementary row operations 2 to matrix 4 1 (ERO), convert matrix A 3 3 B = 2 4 1 Is it…

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Q: 22. || y dA, where S is the first quadrant polar rectangle in- side x + y? = 4 and outside x + y² =…

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Q: fcx) = x+2ー100 2 X +2 -100 Solve this question by the Fixed-point method on the topic of solution of…

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Q: Consider f, g E T° (R") and 0 > 0. Show the following results on the subdifferential. (a) a(0f)(x) =…

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Q: 17. Find scalars a and b such that a(A + B) + b(C + D) = 0. %3D 18. Find scalars a, b, and e such…

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Q: 8. 2 -2 -4 -4 4 1 8. 1 8.

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Q: Find the solution. (y -x+ xy cotx) dx + x dy = 0 A) xy tanx ccosy +secx - xcosx B x siny = cx+ sinx…

A: Since you have posted a multiple question according to guildlines I will solve first question(Q13)…

Q: 17. To each person on the earth assign the number which corresponds to his age. A. bijective 18. To…

A: NOTE: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: Solving a differential equation using the Laplace transform, you obtain s2 + 75 Y(s) gi3 + s² ° f(s)…

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Q: Q 2- use Newton-Raphson method to obtain a root of equation x' - 2x + 3x -5 = 0

A: The given problem is to find the approximate root of given function using newton raphson method.…

Q: Consider the vector space V = C2 with scalar multiplication over the real numbers R and let W and U…

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Q: Question1. Draw the graph of the function f(x) = |x|+\x-1| Question 2. Draw the graphs of the…

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Q: Find the inverse of the following matrix: 1 2 1 2 -1 2 1 1 -2

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Q: Use the last diminisher method to solve the following problem. 1. A piece of property valued at…

A: Given that: The current value of the C-piece when it is the turn of other players P2, P2, P3, P4…

Q: f(x) = x² + 2* – 100 Solve this question by the Fixed-point method on the topic of solution of…

A: Let f(x)=x+2x-100Here x2+2x-100=0 ∴x2=-2x+100∴x=-2x+100∴ϕ(x)=-2x+100Here x 5 6 7 f(x) -43 0 77…

Q: Proofs: Construct proofs to show that the following symbolic arguments are valid.  Commas mark the…

A: There is not any general name for the 6th logical equivalence law described above, but it is an…

Q: Determine whether the following series converges or diverges. Σ >(-1)" sin n=1 Input C for…

A: Convergence of the series,, Using comparison test

Q: Using Laplace transforms, solve the differential equations (D+ 1) y, + (D- 1) y2 = e- (D+2) y, + (D+…

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Q: Suppose you are given that lim(x.4)¬(a,b) [f (x, y) + g(x, y)] = 3 and that lim(=.»)¬(a,b)[f(x, y) –…

A: Given that limx,y→a,bfx,y+gx,y=3 and limx,y→a,bfx,y−gx,y=2. We have to determine…

Q: 10. Let m and n are two positive integers with m > n. Let a be a positive integer. Prove that a2" +1…

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Q: Q4 Evaluate the following integrals cosh? (=) dx -In2 1 - fe 2 - cosh(lnx) dx

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Q: Write down the solution of the differential equation: y+4y +3y 0 if y(0) - 2 and y (0) =3

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Q: find a real root of the equation x + x + x + 7 = 0 by using Bisection method

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Q: Determine the amount of an ordinary simple annuity of $1500 deposited each month for 4 years at 6.1%…

A: We have to find an ordinary simple annuity.

Q: Given: C = 250 + 0.8 Y (6 x 2 = 12) I = 150 G = 300 TR = 100 NX = 100 t =0.25 i) Find the…

A: Given, C=250+0.8 YI=150 , G=300, TR= 100, NX= 100, t=0.25 To find:  i) Equilibrium level of income…

Q: Question 7 Which of the following is a false statement if arbitrary matrices A, B, and C for which…

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Q: QUESTION 19 . (a) Consider the matrix [2 0 A = 0 -1 -4 0 4 -5 0 3 1 Find a basis for Nul A. [-3 3 5…

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Q: Evaluate the integral by making an appropriate change of variables. 5 cos 9 dA where R is the…

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Q: +00 (-1)"(3n + 4) 23n+3(n + 1) Differentiate the function f (x) = x ln(1 + x) to determine the sum…

A: We have to find the sum of series.

Q: Approximate the area under the curve graphed below from 2 = approximation with 3 subdivisions. 1 to…

A: We can solve this using riemann integral

Q: determined the area enclared by * 4ay = x, and y =X +8a 어 %3D 大 x2 4. 9

A: To determine the area enclosed by: 1. 4ay=x2 and y=x+3a 2. 94y2=9-x2 and x29=1-y29

Q: x=ky2 a Figure 1185

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Q: 1 Evaluate dz . 2=4.0 (z – 2.0)° (z² + 25)

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Q: A rectangular box has a square base with edges at least 10 cm long. It has no top, and the total…

A: Given: Square base of the box is 10 cm. Total area of 5 sides is 600 cm sq.

Q: Find the volume of a parallelepiped if four of its eight vertices are P(0,0,0), Q(3, 4, 0), R(0, –3,…

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Q: Find the determinant of the matrix, a b C 2d +a 2e+b 2f +c: ! where a f = 7. A) 35 B) 14 c) 7 D) 21

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Q: 21 Given the matrices, A = (2 -3) and B = -3 2 find the product AB? AB = (-4 - 3) AB = (-7 1) AB =…

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Q: ) Find quadratic least-squares approximation to f (x) = 2*, using ii) Chebyshev polynomials, and

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Q: Problem 2 Let bị = 1 b2 b3 and L a linear transformation from R? to R³ given by L(r) = 1ibı + x2b2 +…

A: Use the given information.

Q: nd the determinant of the matrix, a d e f 5g 5h 5i nere a b ... f = 7. h d e i А) 35 В) 7 c) 14 D)…

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Q: (1) Suppose that f and g are multiplicative functions. Prove that the function F defined by I…

A: Consider functions f and g to be multiplicative functions. To prove that function F defined by…