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Consider the function f(t) = -1tº e C[0,1]. Calculate the norm || || using various norms. A. ||$||1 = B. ||f||2 C. ||fl|3 D. || flloc

User Privard
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1 Answer

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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.

User Mika Fischer
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