Final answer:
The Laplace transform of the function f(t) = 2u(t) + 5tu(t) is 2/s + 5/s^2.
Step-by-step explanation:
The question asks to find the Laplace transform of the function f(t) = 2u(t) + 5tu(t), where u(t) is the Heaviside step function, which is equal to 1 for t ≥ 0 and 0 for t < 0. The first term, 2u(t), represents a constant multiplied by the Heaviside step function, and its Laplace transform is 2/s. The second term, 5tu(t), involves a ramp function (t multiplied by the Heaviside step function), and its Laplace transform is 5/s2. Combining both terms, the complete Laplace transform of f(t) is 2/s + 5/s2.