When does an nth order, homogeneous, Cauchy-Euler equation anty(n) + an-1tn-ly(n-1) + +aity' + aoy = 0 have a unique solution? Justify your conclusion. ***

Q: 1. Let F(x, y) = (1 — y, ½x³ +e³²), and let C with the position vector r be the portion of the…

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Q: Let F(x, y, z) = z tan-1(y²)i + z³ In(x² + 1)j + zk. Find the flux of F across S, the part of the…

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Q: Q1/ Find maximum,minimum ,and saddle point of the surface Z = x³y³ - 12x + 3y + 12.

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Q: There are 15 children in soccer training squad. A team consist of 11 players. If two children can…

A: Given: 15 children To find: Solution

Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz əz (B)If Z…

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Q: 2. Determine the area of the region that is simultaneously interior to the curve r = 2 + cos (30), e…

A: Given that, An area is simultaneously interior to the curve r=2+cos3θ, and exterior to the curve…

Q: 1) Using Laplace transform methods, solve for t20 the following simultaneous differential equations…

A: Given simultaneous differential equation is dxdt+dydt+y=tdxdt+4dydt+x=1 With condition x(0)=1,…

Q: I F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = (x + y2)i + (y +…

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Q: Q5: find the possible solutin area: Max Z= 8x+ 6Y S.To 2X+ 2Y ≤60 2X +4Y ≤ 48 X,Y20

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Q: Find for the function y = cos² 3X + √Sin x dy dx

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Q: Consider the initial value problem y+y=1-₁ y(0) = yo What equation expresses the requirement that…

A: Given differential equation is y'+65y=1−16t and y0=y0. Write the auxiliary equation, which is given…

Q: 63

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Q: The Laplace inverse of 5/(s^4) is: O Non of These O 5^3 Ot*4/5 O 415 51^3/6

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Q: A) Find the Laplace transform of P 0 3

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Q: Find f'(x). 13 f(x) = (6-2x) f'(x) = [

A: Given f(x)=(6-2x)13   To Find: f'(x)

Q: Q5/ change the cartesian integral in an equvalant polor integral then evalute 2x-x² 1 the polor…

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Q: Q4 Calculate the integral Se²y-2x (y + 2x)³ da Where R is the region formed by joining the vertices…

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Q: (m) A represents the quadratic form q(x, y) = x² + 4xy + y²; for what values of (x, y) = R², q(x, y)…

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Q: ∞ Soo 8 2 "dx -7X e

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Q: Approximate the following integral using Simpson's rule. Experiment with values of n to ensure that…

A: Simpson's Rule ∫abf(x)dx≈h3[f(x0)+4f(x1)+2f(x2)+4f(x3)+…+2f(xn−2)+4f(xn−1)+f(xn)] We have…

Q: [4 1 5. Find the eigenvalues and eigenvectors the system X'= 0 4 Lo 0 Use the eigenvalues and…

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Q: 12. Solve the given initial-value problem X' = (₁ − ₁ ) x + ( ₁ + 1₁), X0 = (₁) X ,X(0)

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Q: Solve the ODE y(4) - 4y"" + 8y" - 8y + 4y = 0.

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Q: (f) What is the first-order condition implied by unconstrained maximization of I1 X 1333 X, where x…

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Q: Q2: a group of 6 boys and 4 girls, in how many way four children can be selected such that at least…

A: Given is a group of 6 boys and 4 girls.   To Find: Number of ways four children can be selected such…

Q: Q8. Solve: log₂x + log₂ (x + 2) = log₂ (x + 6)

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Q: Let _X=R². Find M² if M= {(a,1)}.

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Q: Solve by the Lapace Transform: y(t) + 4 y(T) (t - 7)dt = 2t [₁ dT

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Q: [2 sin 2t +20 + ecos4t]

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Q: In Numerical differentiation, explain and solve a sum using Newton's forward method clearly with…

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Q: using data on Y and x estimate the 2 regression equation what is the are the value of R² ? Yi =…

A: Given the data on x and y To find the regression equation of line. Also find the value R2

Q: 1. Let k> 0 be a given number. Consider the solid bounded above x² + y²+z² = 2k² and bounded below…

A: The given problem is to set up an double integral in Cartesian coordinates that gives the volume of…

Q: Find the local maxima, local minima, and saddle points of the function, f(x, y) = x³ + 3xy + y³

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Q: I+J

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Q: Evaluate the following double integral using the composite Simpson's 1/3 rule with one interval in…

A: To find- Evaluate the following double integral using the composite Simpson's 1/3 rule with one…

Q: sin x cos x) (2 -

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Q: ! (9) Let K be integer ring module 12 and let I-([4]) and J-([6]) be ideals of K. Then ([0]) (i) I +…

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Q: a On Monday, Nikita and Peter cycle and Reeta walks. On reaching the point four-fifths of the way…

A: (a) according to question distance between school and home is d=5 km walking speed s1=4 kmhr cycling…

Q: A thermometer is removed from a room where the temperature is 70° F and is taken outside, where the…

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Q: For the values 2, 4, 6 thee variance is 1.66 2.77 2.11 O 1.33 O 2.66

A: We have to find the variance from the given data.

Q: 14 1 01 5. Find the eigenvalues and eigenvectors the system X'= 0 4 1 1 [X]. lo o Use the…

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Q: change the cartesian integral in an equvalant polor integral then evalute 2x-x² 1 the polor integral…

A: To change cartesian equation into polar, we use following substitutions x=r cosθy=r sinθdydx=r dr dθ

Q: Find the number of positive integers ≤ 1000 that are not divisible by 5, 13, or 31?

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Q: Q2/ Reversing the order of integration fxsinydydx.

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Q: Consider M(x, y) + N(x, y) = 0. (a) Suppose we can find a function F = F(x, y) so that Fr F(x, y) so…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: The modulus of 5 + 4i is * O-41 O-√41 O√41 041 The conjugate of (i-i²)³ is O-2-21 2+2i -2+2i Oi-1

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Q: ring with identity and I be ideal of R. Then I is prima and only if every invertib R/I is a…

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Q: Express in p/q form 1) i) 0.005 ( bar for 005) ii) 1.3 ( bar for 3) iii) 4.78 ( bar for 8

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Q: 4. Determine whether the vector functions are linearly independent. Show your work. 1 4². 2t 8t 2

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Q: Write Fourier series for the function y=4n-k T≥X≥0

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