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Q: Suppose that liquid flows into a tank at a variable rate of q(1) litre per second. It can be shown…

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Q: -1)" Σ iven: In(1+ x) = if |æ| < 1. n + 1 n=0 Find the Maclaurin series for f(x) = x ln (1 +

A: Macluarin series expansion of the function

Q: Find AB such that [3 1 21 T-1 A = 2 1 2 and B =|4 [1 2 2] -2 -5]

A: The solution is given as

Q: Find the unit vectors that are perpendicular to U = and V =,

A: Given the vectors U→=2, 3, 4 and  V→=-1, 3, -5 We will find the unit vectors that are perpendicular…

Q: f (x) = e2* if x> 0 The Fourier transform of the function: 0if x<0

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Q: If A = {x:x [B| None of these Option 3 O Option 4 |A| = |B| |A| < |B|

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Q: 3- Find an equation of the Plane perpendicular to the line through (2,2,-9) and (7,-1,3) and…

A: To Find: Equation of plane perpendicular to the line through the points (2,2,-9) and (7,-1,3) and…

Q: for -π<x<01 04. Find the Fourier series for the function: ƒ(x)= for 0<x< T

A: Fourier series of the function

Q: -i2t +e 21.Find the value of following (a) (1+ i)'0° (b) 2

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Q: Show that y = x is a solution of the differential equation x^2 y” – (2x + x^2 )y’ + (2 + x)y = 0,…

A: The solution is given as

Q: y′′′ − 2y′′ − y′ + 2y = e^(−t)sin t by variartion of parameter

A: Given equation  y'''-2 y'' - y' +2y = e^(-t) sin t, say (1)  First we'll find the complementary…

Q: Г16 If n is a positive integer, then 4 36 is -16 [16 (Hint: Diagonalize the matrix 4 36 first. Note…

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Q: 4. Let X be the set {a, b, c, d, e} and Y be the set{g,h, i,j,k}. A description for the functio f:X…

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Q: Check that the system Ax b with 1 3 1 A -1 and b 1 16 - 14 5 - 6 10 3 is inconsistent (note the rank…

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Q: What is the trial particular solution for g (x) = (x2 – 1) sin 2x? | O Yp (Ax? + Bx – C) sin 2x +…

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Q: Let f(x) 1- (2г — 3)3 (a) Find the Taylor series representation for f about x = 1.5 that is valid…

A: This is a problem of Taylor's expansion.

Q: other than the real root 2o , find the other 7 the equaton z 3 -용 +i and- 号- and 2 C. 늘 +i and 수 -…

A: Solution

Q: 1. Consider e" for all x E R. n! n=0 a. Determine the power series representation of f(x) = xe-5x…

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Q: Find the three cube roots of -8i. Express your answers in polar form and the convert them into…

A: To find the cube root of -8i Let z = -8i

Q: 3. Find the Taylor series expansion of sinhx about x=0 and its interval of convergence. Then find…

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Q: 4- Determining Whether a 3 x 3 Matrix A is Orthogonal or not. - A = 2 -1 2 2

A: This is a problem of linear transformation.

Q: Consider the figure below. Triangle A'B'C' is a projection of triangle ABC. • Points C, C', and Q…

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Q: rotating the region R about the y-axis, not the x-axis. i got 62*pi/5

A: The given answer is correct, i.e.,   V=1277π cubic units

Q: 4. Any non-empty set A and its power set P(A) do not have the same cardinality (i.e. there exists no…

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Q: Jae sIT expressed what IS rectangular firm? in A. -I tiì C - B 1- D. Ja -i

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Q: 1 Find the Inverse Laplace Transform of s2+2s + 10 A -e 'sin9t 3 -e-'sin3t 3 3t e"cost (D 3 "cos3t…

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Q: Use the substitution x = e' to transform the given Cauchy-Euler equation to a differential equation…

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Q: (-1)"(n + 2) 2n+1(n + 1) Compute the exact value of n=0

A: The ratio test can be used to assess if a series is converging or diverging. The following are the…

Q: Evaluate the triple integral In(1+ Vr2 + y? +z?)dzdydr.

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Q: Let f : R? → R² be the linear transformation defined by 0 5 f(x) 2 3 Let B {{1, 2) , (3, 5)}, с…

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Q: Based on your understanding, solve the following problem Find the particular solution for the given…

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

Q: Solve the differential equation with appropriate method, Finalize answer equated to y. dy/dx =…

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Q: 5. a. Write in your own words a definition of a complex numbers and Modulus of the complex number.…

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Q: 2x Let f(r) (1 – 2²)² ° (a) Express f(r) as a power series. n (b) Using the result in la, find the…

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Q: 7. If 300 cm³ of material is available to make a box with a square base and an open top, find the…

A: Assume side of the square box is x and height is y. Hence, volume of the box is given by…

Q: 1. (y²+ 6x²)dy –- 4xydx=0

A: The solution is given as

Q: Find the solution to the initial value problem (1+ a®)y/ + 9®y = 9a? subject to the condition y(0) =…

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Q: WHICH OF THE FOLLOWING ARE DISCRETE PROBABILITY DISTRIBUTION? IF IT IS NOT A DISCRETE PROBABILITY…

A: Solution: Probability function is a function which assigns probabilities to the values of a random…

Q: Find the solution of h (x) = e sin r = 2 using False Position method between 3.0 and 3.1 (use these…

A: To find the solution by using False position method between 3.0 and 3.1

Q: Q7. Solve the Cauchy-Euler equation (i) 4.x²y" + 4.xy' – y = 0. (ii) 4x²y" + y = 0.

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Q: Identify and sketch the graph of the following equations in R³ (a) x2 + 4y² + z² – 8x + 16y – 2z +…

A: we can add or subtract same amount from a equation to simplify equation. The logarithm function…

Q: GENERAL MATHEMATICS Identify the domain and range of the following logarithmic functions. y=log…

A: Given function is y=log6x-1-5

Q: Find the indicated powers of the given complex number. Express the result in polar form, then…

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Q: Let 7,V be a projection af the Vect or space. Accordling to this: Show that every Xe Im (T) for…

A: The given problem is related with projection. Given that T is a projection of the vector space V .…

Q: Find the first fundamental form of surface of revolution?

A: Suppose M is a surface determine by , Xu , v ⊂ E3. Suppose αt is curve on M , where t ∈ a , b. Here…

Q: Show that if a|m and a|(ms+nt) for some integers a≠0, m, s, n, and t, then a|nt.

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Q: 1. Solve the heat conduction equation with the prescribed initial and boundary conditions: Uxx = Ut…

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Q: dy Differential equation = f(x) · g(y) can be solved by separating variable as - = f(x)dx. dy + 1+y?…

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Q: x + 2y + z – t= 5 -x + y+ 2z + 2t = 8 2 4x + 4y + 3z+ 4t = 22 2 1 x + 5 52+t= 3

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

Q: Calculate the Taylor polynomials T2 and T3 centered at a = 0 for the function f(x) = 14 tan(x). (Use…

A: The given function is fx=14 tanx. Now we have to find the 2nd degree and 3rd degree Taylor's…