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Find the Laplace transform of f(t) = 2๐‘’7๐‘ก-2Question 4Select one:2๐‘’-2๐‘ +7-2๐‘’-2๐‘ +72๐‘’-2๐‘ -72๐‘’2๐‘ -7

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Solution

It seems like there's a bit of confusion in your question. However, I'll try to guide you through the process of finding the Laplace transform of the function f(t) = 2e^(7t) - 2.

The Laplace transform of a function f(t) is given by the integral from 0 to infinity of e^(-st)f(t) dt.

  1. First, we'll break down the function into two parts and find the Laplace transform of each part separately.

  2. The Laplace transform of the first part, 2e^(7t), is given by the integral from 0 to infinity of e^(-st) * 2e^(7t) dt. This simplifies to 2 times the integral from 0 to infinity of e^((7-s)t) dt.

  3. The Laplace transform of e^(at) is 1/(s-a), so the Laplace transform of 2e^(7t) is 2/(s-7).

  4. Similarly, the Laplace transform of the second part, -2, is given by the integral from 0 to infinity of e^(-st) * -2 dt. This simplifies to -2 times the integral from 0 to infinity of e^(-st) dt.

  5. The Laplace transform of a constant c is c/s, so the Laplace transform of -2 is -2/s.

  6. Therefore, the Laplace transform of the function f(t) = 2e^(7t) - 2 is 2/(s-7) - 2/s.

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