Solve the problem.For f, g in C[a, b], set
=
.Show that
defines an inner product of C[a, b].
What will be an ideal response?
Answers will vary.
Inner product Axioms 1-3 follow from elementary properties of definite integrals.
Axiom 4: =
dt ? 0.
The function [f(t)]2 is continuous and nonnegative on [a, b]. If the definite integral of [f(t)]2 is zero, then [f(t)]2 must be identically zero on [a, b]. Thus, = 0 implies that f is the zero function on
Mathematics
You might also like to view...
Graph the equation. -
= 1
A.
B.
C.
D.
Mathematics
Decide whether the given number is a solution of the given equation.Is 14 a solution of p - 1 = 13 ?
A. yes B. no
Mathematics
Write the phrase as a variable expression. Use x to represent "a number."41 subtracted from a number
A. x - 41 B. 41 C. 41 - x D. 41x
Mathematics
Multiply and simplify.x-9 ? x3 ? x-8
A. x14
B. x20
C.
D.
Mathematics