Let V be the vector space C([-1,1]) of continuous functions on interval [-1,1] equipped with the scalar product (f\g) = f f(t)\g(t)dt. a) Find the length of f(t) = e ¹0t and g(t) = e-1⁰t in V b) Find the angle between fand g from (a) c) Is this angle similar to any angle you know?

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Chapter2: Second-order Linear Odes
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Let V be the vector space C([-1,1]) of continuous functions on interval [−1,1] equipped
with the scalar product
(f\g) = f, f(t)\g(t)dt.
a) Find the length of f(t) 10t and g(t) = e
-10t
= e
b) Find the angle between fand g from (a)
c) Is this angle similar to any angle you know?
in V
Transcribed Image Text:Let V be the vector space C([-1,1]) of continuous functions on interval [−1,1] equipped with the scalar product (f\g) = f, f(t)\g(t)dt. a) Find the length of f(t) 10t and g(t) = e -10t = e b) Find the angle between fand g from (a) c) Is this angle similar to any angle you know? in V
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