If-you-have-a-real-continuous-function-f-x-If-you-take-a-distance-between-f-x-and-f-x-1-what-is-the-average-distance-within-a-x-b-

Question Number 6610 by Temp last updated on 05/Jul/16

If you have a real continuous function f (x),

If you take a distance between

f (x) and f (x + 1), what is the average

distance within a ⩽ x ⩽ b ?

Commented by Temp last updated on 05/Jul/16

let the distance be :

d = \sqrt{∣ f (x + 1) - f (x) ∣^{2} + ∣ (x + 1) - x ∣^{2}}

d = \sqrt{∣ f (x + 1) - f (x) ∣^{2} + 1}

Commented by Yozzii last updated on 05/Jul/16

d_{a v g} = \frac{1}{b - a} \int_{a}^{b} d d x

d_{a v g} = \frac{1}{b - a} \int_{a}^{b} \sqrt{{(f (x + 1) - f (x))}^{2} + 1} d x

Commented by Temp last updated on 05/Jul/16

I thought so, thank you!

Commented by Temp last updated on 05/Jul/16

is it {(f (x + 1) - f (x))}^{2}

o r

∣ f (x + 1) - f (x) ∣^{2}

? ?

Commented by Yozzii last updated on 05/Jul/16

T h e y a r e e x p r e s s i o n s e q u a l i n v a l u e

s o e i t h e r n o t a t i o n i s a p p r o p r i a t e .

I w a s t a u g h t t h a t f o r m u l a u s i n g p a r e n t h e s e s .

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