State, with explanation, the truth value of the following statements. x²-x-2 a) x = 2 is a vertical asymptote of f(x)= 2 x²+x-6 b) f(x)=e* has no horizontal asymptotes.

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A: Given problem:- ∫arctan(y)/y3 dy

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Q: Solve the following Differential Equations with Laplace Transforms y" - 6y' + 15y = 2 sin (3t), y…

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A: solution

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A: We can evaluate the given integral by using the method of partial fraction.

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A: Note: Every options given by the question are incorrect. I am 100% sure about it.  The correct…

Q: (2x-1) dx 3 2x²-x²-27x +36 f

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Q: ∫0.00202003x^4/4-0.0185672x^3/3-0.0937054x^2/2+2.17676x+C

A: We have to solve it. But it's not clearly mentioned that, either We have to find integration or…

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A: Follow the procedure given below.

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A: Divergent

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A: Let's solve given integral.

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Q: ?What is order of the equation (y"+2y+3=0) Second order O First order O Zero order O Third order O

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Q: Solve step by step in digital fe 6x - 1 a) lím x→ 1/ 2x - 6 b) lím X-00 x² - 9

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A: The answer is given below:

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Q: Which of these series, if either, diverges? ∞ - 1)k 1. II. Σ(-1)^ (77) K²+1 k=1 k k=1 A. I only B.…

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Q: Which of these series, if either, converges conditionally? 1. - (−1)k k=√k (-1)k II. Ÿ (- 1)*…

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Q: ifferentiate the funtion y = 2 csc (1-3x)

A: Giveny=2cosec(1-3x)Aim: dydx

Q: Solve the following Differential Equations with Laplace Transforms y" - 6y + 15y = 2 sin (3t), y (0)…

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Q: cos e de sin² 0 + 4 sin 0-5

A: To evaluate the given integral.∫cos θ dθsin2 θ+4 sin θ-5

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Q: If real and imaginary part of an analytic function are constants. Show that the curves given by u…

A: Function f(z)=u(x,y)+iv(x,y) is said to be analytic in a region R if:-(i) ux,uy,vx,vy exist and(ii)…

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Q: + d) y(x) = ce c) y(x) = c₂e²x + c₂ex Q3) Evaluate L (e-2t sin4t): 4 4 5+2 5+2 d) a) 5²+45+20 b)…

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Q: 3-x x F(x) = (₂ + 1 (a) Find lim f(x) and lim f(x)? x-2+ x-2- (b) Does lim f(x) exist? why? x-2 x 3

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Q: 6. Find the symmetric equation of the line parallel to ở = (1,4, 6) + t(−2, 4, 7) that intersects…

A: Given problem:- 6. Find the symmetric equation of the line parallel to r = (1,4,6) + t(−2, 4, 7)…

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Q: 1.If f(x,y) cos(4x-2y)+ln(y² -2x) find £xy fx fxy,

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Q: | 1) 2Ln(√x + 3) + 2Ln(√x − 1) = Ln(6x - 7) 2)3x+2 = 27

A: This question is related to solution of equations, we will solve it using given information.

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A: Given that infinite series is

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A: Follow the procedure given below.

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A: The inverse laplace tranform L-11s-73

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Q: c) L-1, 4s² - 21s+ 30 (s² - 6s+13) (s – 4) -

A: Above question is solved.

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A: You must have an idea about basics of derivative in order to understand this problem.

Q: The diversity of a population that contains two species can be measured by the Gini-Simpson…

A: The diversity is given by H(p)  H(p) = 2p(1-p)   H'(p) = d/dp(2p(1-p)) H'(p) = 2(1-p) -2p H'(p) =…

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Q: * What is inverse Laplace for 1 (s + 1)² + 1 y (s) =

A: option 2

Q: 3x + 1 Evaluate (x-1) (x+2) dx using Partial fractions.

A: This question can b solved using the concept of partial fractions.