Final answer:
The question seems to contain a typo regarding the function f(t). If assumed to be a constant function with the correct form, its norms over the interval [0,1] can be expressed as L1, L2, and L-infinity norms.
Step-by-step explanation:
The student has asked for the calculation of the norm of a function f(t) = -t0 e C[0,1] using various norms. However, there seems to be an issue with the function's description as -t0 would simplify to -1, which is a constant function. Assuming it is indeed a constant function, its different norms over the interval [0,1] would be:
- ‖f‖1 which represents the L1 norm or the integral of the absolute value of the function over the interval [0,1].
- ‖f‖2 representing the L2 norm or the square root of the integral of the square of the function over [0,1].
- ‖f‖∞ which is the L-infinity norm or the maximum absolute value of the function over [0,1]. This is straightforward for a constant function.
Without more context or a correct function form, it is not possible to give the specific calculations for each norm.