Question

Let V be the vector space C[0,1] consisting of all real valued continuous functions on the unit interval [0,1]. For any f and g in V, let the inner product of f and g be defined by egin{equation} langle f, g angle = int_0^1 f(t)g(t)dt end{equation}Verify that this is an inner product on V. If $f(t) = t$ and $g(t) = e^t$, are f and g in V. If they are then compute $langle f, g angle$

          Let V be the vector space C[0,1] consisting of all real valued continuous functions on the unit interval [0,1]. For any f and g in V, let the inner product of f and g be defined by
egin{equation*}
langle f, g 
angle = int_0^1 f(t)g(t)dt
end{equation*}Verify that this is an inner product on V. If $f(t) = t$ and $g(t) = e^t$, are f and g in V. If they are then compute $langle f, g 
angle$

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Let V be the vector space C[0,1] consisting of all real valued continuous functions on the unit interval [0,1]. For any f and g in V, let the inner product of f and g be defined by
eginequation*
langle f, g
angle = int0^1 f(t)g(t)dt
endequation*Verify that this is an inner product on V. If f(t) = t and g(t) = e^t, are f and g in V. If they are then compute langle f, g
angle

Added by Tammy H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Supreeta N

07/18/2023

Step 1

First, we need to verify that the given definition of inner product satisfies the properties of an inner product on V. The properties are: a) Linearity: (af + bg, h) = a(f, h) + b(g, h) for all f, g, h in V and scalars a, b. b) Symmetry: (f, g) = (g, f) for Show more…

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Let V be the vector space C[0,1] consisting of all real-valued continuous functions on the unit interval [0,1]. For any f and g in V, let the inner product of f and g be defined by <f,g> = ∫[0 to 1] f(t)g(t)dt. Verify that this is an inner product on V. If f(t) = t and g(t) = e^t, are f and g in V. If they are then compute <f,g>

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