Identify any vertical asymptotes of the function: 5x² f(x) = x² - 16 If there are none, briefly explain why.

Q: For any irrational number a show that the fractional parts of an, which is denoted by {an), are…

A: To find: For an irrational number, the fractional part of nα for n ∈ N is uniformly distributed in…

Q: 1. dy +4- dt 5y = 0 dt2 y(0) 11, y'(0) = -7 =

A: To solve the given IVP first we will rewrite the given differential equation and write it's…

Q: Find the remainder when 7305 is divided by 5.

A: We have to find the remainder when 7305 is divided by 5

Q: Write the general conic

A: The standard equation of horizontal ellipse centered at h, k with semi major axis length a and semi…

Q: Solve each of the following by Laplace Transform: dy 1.) +2- + y = sinh 3t – 5 cosh 3t ; y (0) = −2…

A: We have to find the solution to the given equation using the Laplace transformation.

Q: in solving for the area bounded by y = x, y = 2x and x + y = 6 using a vertical element, he total…

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Q: 6. dy dx 4x + 3y 2x+y

A: Solution :-

Q: In Exercises 1-3, find the solution of the given IVP. 1. +4- -5y=0 dt 2. 9(0) = 11, y'(0) = -7…

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Q: 1. dy dx x + y x

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Q: The area of a circle varies directly as the square of its radius. A circle of radius 4 cm has an…

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Q: dY = 3) Y, dt 3 (a) find the general solution; and (b) find the particular solution for the IC Yo=…

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Q: 2. A vehicle starts from rest and its velocity is 8.0 measured every seconds for 8 seconds, with…

A: In this question, the concept of the Simpson Rule is applied. Simpson Rule ∫abfxdx≈h3∑j=1n2…

Q: (6) In our discussion about Fibonacci sequence, we said that Fibonacci numbers occur in the species…

A: To Find: An example of a species of flower having 13,21,34, and 55 petals.

Q: dx d. de. f(3x + 2)5 dx f sec²x

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Q: Determine the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 4z² : =…

A: Given equation: ellipsoid: 4x2+y2+4z2=4; half-cone: y2=x2+2z2 To find: parametric equations for…

Q: جليلة Let I = [= 1,₂1] ISR interval w that I is negligible Set.

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Q: Use Laplace transform to solve the partial differential equation: o'y dy +xt where y(x,0) = 0,…

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Q: Apply the formula deduce that (x) log x + [A(n) () = 2x log x + 0(x) n n≤x as x→∞o, where y is…

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Q: 1. Consider the following table. X₁ 4.0 4.2 4.5 4.7 5.9 5.1 5.5 167.53 195.14 6.3 256.73 y 102.56…

A: We will use the basic knowledge of numerical analysis to answer both the parts of this question…

Q: 13. x1 + 3x2 + 3x3 = 13 2x1 + 5x2 + 4x3 = 23 2x1 + 7x2 + 8x3 = 29

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Q: 6-4 - Let X and Y be normed spaces and Z be a closed subspace of X. (a) Let F E BL(X,Y) and Z C…

A: See that this is a post with multiple questions, i.e., two or more unrelated questions. Here,…

Q: Use the induction argument to prove that 1+2+ + n = n(n+1) 2 for all natural numbers n ≥ 1.

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Q: A milk truck carries milk with density 64.6 lb/ft 3 in a horizontal cylindrical tank with diameter 6…

A: We will find  force on a horizontal slice and then integrate it to find total force on the plate

Q: art 2 6. determinants of the following matrices 1 2 -1 2 1 5 0 3 1 6 Find the Evaluate D = 3 1 -2 0…

A: D=12-1230151-203-2-416

Q: 4 The shaded region in Figure 3 is bounded by curve y=x+ and line y = 5. X y X=-1 y=x+- y=5 (1,5)…

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Q: sorry also why have you put 1/270 x the matric i dont see that in the formula ? how is the final…

A: Solution

Q: . Determine the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 4z² =…

A: We will find intersecting curve and then parametrize it .

Q: dy 6. dx 4x + 3y 2x+y

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Q: 3.11 Definition A square matrix is nonsingular if it is the matrix of coefficients of a homogeneous…

A: In the given problem the concept of rank of a matrix is used to obtained the cases for the existence…

Q: Given that (x' (t)-x(t) + y'(t) - z(t) = 3 y(t) + y'(t) + z' (t) = 2 x(t) + y'(t) + z' (t) = 2 TT…

A: We have to find the value of zπ2

Q: Translate the phrase to mathematical expression. "The total of the square of a number and the…

A: Let x be a number, we have to write the mathematical expression of " The total of the square of a…

Q: Radius of curvature for the curve T y = 4 sin x-sin 2x at the point x = is 2 √5 (a) (b) 3√5 4 4 (c)…

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Q: Q3] ( The specific volume of a superheated steam is listed in steam tables for a various…

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Q: Simplify the following using De Moivre's Formula 1. (1 - 1)³ 2. (2/2² - 1/³i) ²2 2

A: For simplifying the given problems first we will convert it into polar form then we will use the De…

Q: X 7.47 f(x) 1.93 7.48 1.95 7.49 1.98 7.5 2.01 7.51 2.03 7.52 2.06

A: The given table is  To find: The integral value of f(x).

Q: Determine the derivative of the following implicit function on a separate sheet of paper, assuming…

A: Here the given implicit function is                                          x3y2+xy3=2x2 We have to…

Q: Let A be an n x n matrix. Let n-1 c(z) := det(zIn − A) = 2² - Σckzk - k=0 be the characteristic…

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Q: Find all solutions of the Diophantine equation 1245x-365y = 4567

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Q: 3. Let R(t) = (t²,1 - t², t) and r(t) = cost. Determine the parametric equations of the line tangent…

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Q: 6. dx 4x + 3y 2x+y

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Q: 2. Ifƒ (x, y) = log (x² + y²), then f +f, is equal to yy 1 (a) x² + y² (b) 0 y²-x² (c) (d) • (x² +…

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Q: If S., t, = \n(n+1)(n + 2)

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Q: Using "Newton's progressive method from the table below, the approximate value of the function…

A: Introduction: Given some points, polynomials may be used to estimate difficult curves, consisting of…

Q: Determine the derivative of the following implicit function on a separate sheet of paper, assuming…

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Q: Find all solutions of the Diophantine equation 1245x-365y = 4567

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Q: 3. For the linear system - (²) Y dt (a) find the general solution; and (b) find the particular…

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Q: ) In our discussion about Fibonacci sequence, we said that Fibonacci numbers occur in the species of…

A: as we know, fibonacci numbers occurs in the species of flowers in relation to their numbers of…

Q: OLVE THE FOLLOWING HOMOGENOUS LINEAR DIFFERENTIAL EQUATIONS. 4. (D6 + 10D4 + 25D²)y = 0 5. (D³ - 2D…

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Q: 3. (tan 45°) (cos30°) - (cot45°) (sin 60°)

A: