Question

Write a formula for f(t) as a sum of Heaviside functions. Type u for the Heaviside function that jumps at c (don't type u(t) ).

F(t) = t, 0 ≤ t ≤ 3
2t−3, 3 < t ≤ 4
5, 4 < t

Answer 1

The formula for the piecewise function f(t) in terms of Heaviside functions is f(t) = t·u(t) + (2t - 3)·(u(t-3) - u(t-4)) + 5·u(t-4).

Step-by-step explanation:

The student is asking for a formula for a piecewise function f(t) in terms of Heaviside functions, which are used to represent functions that have jumps or steps at certain values. We can define the function given as f(t) = t for 0 ≤ t ≤ 3, f(t) = 2t - 3 for 3 < t ≤ 4, and f(t) = 5 for t > 4, by using Heaviside functions u(t - c), which are equal to 0 for t < c and 1 for t ≥ c.

The formula for f(t) using Heaviside functions is:

f(t) = t·u(t) + (2t - 3)·(u(t-3) - u(t-4)) + 5·u(t-4).

This represents the function as a sum of terms that are 'activated' or 'deactivated' by the Heaviside functions at the specified points.