Find the Laplace transform F(s) = L(f(t)) given f(t) = 0, t < 6 %3D 1(t-6), t> 6 F(s) = 120e^(-2s)/(s^6)

Q: (Implicit differentiation). Consider the curve 1/t + 1/s = 1 Find d/s = d/t Find d/t = d/s Show…

A: Given that: 1t+1s=1

Q: Find the derivative of arctan(x² + 1) -2x O f' (x) = -2a2 – a4 2x f' (æ) = x² +2 2x f' (x) x4+2x²+2…

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Q: If f is continuous and f(x)dx=10 on the interval [0,4] find xf(x^2) dx on the interval [0,2]

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Q: f(z) = (x+iy)^3 is analytic or not

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Q: Find an equation of the tangent line to the given curve at the specified point. 4x y = - x + 3 (1,…

A: according to our guideline we supposed to do only the first question if you want any particular…

Q: Attached below is a description and the differential equations problem/question: What is the…

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Q: Find f if f"(t) = 2et + 3 sin(t), ƒ(0) = 2, ƒ(π) = 5. f(t) = = 2e^t-3sint+ (2e^(pi) - 5)/(pi)t

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Q: (1/x 15. h(x) = Sy sin't dt

A: hx=∫21xsin4tdt

Q: 39 Find the value of c that satisfies Rolle's theorem for f(x) = 2x^4 -16x I 5. You are a…

A: Given query is to find the the value of c.

Q: Find the derivative of f(x), where ƒ'(x) = 3 f(x) = =1² 1-3x sin(t) - dt. 1+ t²

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Q: Find the first derivative for each tunction. O fex) =3x"(ax^-1) O g4) = (t+)(t? -t +i) 3.

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Q: Find the differential of the function  G(x) = sq rt (5(x^4)+cos(2^x)).     all under sq root!! :)…

A: Given Function is, G(x)=5x4+cos(2x)

Q: 1 6. Find the derivative of f(x)= 1 at the point 8, Vx+1

A: Given

Q: Let f(x) = 6x* /T + f'(x) =

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Q: parametrize the path that follows the graph of the function y=e^x from (0,1) to (1,e)

A: We parametrize the path that follows the graph of the function y=e^x from (0,1) to (1,e).

Q: Let F(x) = ₁ In(cott + 10) dt, Find F'(x)

A: The given problem is to find the derivative of function F(x). Given F(x) is Integral Function. We…