1 Q.3 Evaluate ((s+2)(s² +4)]

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A: Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for y...

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A: This is a question of application od derivative and geometry.

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A: Let us solve the integral using substitution method in the next steps.

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A: Please post the multiple parts separately.I answered here first three sub parts as per our policy.

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Q: 4 f4* u lt - i) + (+1) u(t -)

A: Some of the properties of the Laplace transform   Lu(t-c)=e-cssLf(t)+g(t)=F(s)+G(s)L[af(t)]=aF(s)

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A: Given relation is R = {(a, b) : a ≤ b3}

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Q: xct) = 3(t/4) e

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A: The root of the equation: f(x)=0 lies in the interval: a, b, if f(a)f(b)&lt;0. The bisection method ...

Q: (1 – x²)y - 2ry' + 2y = 0

A: given differential equation 1-x2y''-2xy'+2y=0                ...i let the solution be of the form y=...

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Q: ( optional). Let f be continuous on [a, b] and differentiable in (a, 6). Show that if lim f'6) = A, ...

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Q: 1. X = {1, 2, 3, 4, 5} and Y = {3, 4}. Let's define a relation R in a set P(X), by a formula: (ARB) ...

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