(4) Σ n=2 3n η3 x 5m (4)

Q: Integrate. √ ( 7x² + 2/17 - 0²³) 0 3x 4+ dx = 0 +C

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Q: Numeric Response 1. The Math Department is made up of ten math teachers, 4 male teachers and 6 fema…

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Q: kp - x² + 5x²+4x = 12+ + 30e to) = (0) (250)P x(0)=1, x'(0)=3 Solve the above IvP and then find OH…

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Q: 4 (x + Jy) dxdy へ。 1 1.

A: In the question we have to evaluate the double integral.

Q: x+2 Q2) k(x) -Vx – 2 , n(a) = x²(x² + 1)¬1, mx) %3D 3-x Find a formula for (n oko m).

A: A composite function is a function that depends on another function. A composite function is created…

Q: (3x²-1) 5x3-5x+13 - dx equals In 15x³5x + 13| + c In 15x³ - 5x + c 5 O 1 In 15x³ - 5x + 13| + c 5 In…

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Q: (a) Show that: (i) dim R" = n (ii) dim R2×2 (iii) dim Pn = n+1 = 4

A: Basis of a vector space: Let us consider a set S⊂V(F) is said to be basis of vector space V over…

Q: Find C (x.y) if C(x,y) = 8x? + 12xy – 14y? + 4x- 11y – 112. Cx (x.y) = D

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Q: 1 0 2 Find x, if [x -5 -1] 0 2 1 2 0 3 4 =0. %3D

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Q: 1. y = ao Σm=o(−1)m(2m + 1)x2m + ai Σ=o(-1)"(m + 1)x2m+1

A: 1+x2y''+6xy'+6y=0

Q: Given z = (1 + iv3)100, then %3D find the value of Re (z) / Im (z).

A: The solution is given as

Q: Obtain the value of P3 (x) using Rodrigues' formula d" P,(x) = (x² – 1)" (2")n! dx"

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Q: Write the general solution of the ODEs by finding two power series solutions about the ordinary…

A: The differential equationTo find the series solution about x=0, ordinary points.

Q: Using Rodrigues' formula for Pn(x), (T) (i) Pn(-x) = (-1)" P₂(x) cl

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Q: x² + y² = (3x² + 2y² – x)², (cardioid) 0, y 0.5 -0.5 0.5 1 -0.5

A: Giv:    x2 + y2 = ( 3x2 + 2y2 x )2     Point: ( 0 , 1/2 )

Q: (x)u[ S -dx 陇

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Q: х+1 .2 (x – 1)

A: LetI=∫x+1x2x-1dxTake partial fractionx+1x2x-1=Ax+Bx2+C(x-1)…

Q: Solve the equation (i) 22r +1 = 20, %3D 54y-1 125+3 (ii) 25 252-y

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Q: e3z I dz (ez + e 5z )2 II

A: Introduction: The Ortrogradsky's method is used in finding integration when the integrand is a…

Q: 1. Find a power series for each of the following, centered at a = 0 for parts (a) (d) and centered…

A: (a) Given data: The given expression is 4/(1+2x). The expression for the power series of the given…

Q: ut. (b) 710 - 76 72 (c) m*n (e) m m2 ÷ m* (f) -25A

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Q: (a) e2tsin (wt +t/6)

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Q: Ο Σ n=1 (-5) " 32n

A: I have used simple trick of geometric sum.

Q: Find t(4)(n) for the function t(n)=3n-1/3 +2n5/3

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Q: Evaluate. √26 S 6x²√1+x² dx √26 S 6x³√/1+x² dx = 0 (Type an exact answer.)

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Q: (2) The number q of roller blades a firm is willing to sell per week at a price of Sp is given by q…

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Q: L{e*u(t – 1)}

A: In this question, we have to evaluate Laplace transform of the function e-tu(t-1) here we use the…

Q: -2 -1 1 2 p(x) 1/3 k 2k 2k 1/6 : E(x) О з0/7 О 7/30 О 7/30

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Q: Actual commuting time in minutes (T) depends on both the weather, and the length of commute. Suppose…

A: From the tables  We can the value at X=0 and Y= 1 is 15  So n(X=0,Y=1)= 15

Q: ) Find the general Solution of PDE : 3/2.2

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Q: (a) (b) 12 in (1 + √5) In 3 In 2 (c) (24) (d) - In (1+√3) =)/In (1+ √5) √ √2+1 dx = ? In 2+√3

A: The given integral is

Q: (9) Let X z b(n,) and E(3x) = E(3– 5x) find n.

A: