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math

help me do this.

Original post by huvaxshatra

...

\displaystyle f(x)= \left\vert x-\frac{x}{a} \right\vert

?? Is

a

a constant?

(edited 7 years ago)

Reply 3

_gcx

Study Forum Helper

f(x) = |x - \frac{[x]}{a}|

(

[x]

being the floor function of

x

) or

f(x) = |x - \frac{x}{a}|

(edited 7 years ago)

*(s)

solved

Original post by _gcx

f(x) = |x - \frac{[x]}{a}|

(

[x]

being the floor function of

x

, in which case it cannot be differentiated) or

f(x) = |x - \frac{x}{a}|

l mean

Reply 6

_gcx

Study Forum Helper

Original post by huvaxshatra

l mean

Is this part of a question? If so, can you take a picture of the question?

The derivative of the floor function is 0 at non-integers, and undefined (some sources I've seen express it as

\infty

) at integers, I'm sure.

Reply 7

username3112014

if a=1/2 we can find the answer

(edited 7 years ago)

Reply 8

username3112014

Original post by _gcx

Is this part of a question? If so, can you take a picture of the question?

The derivative of the floor function is 0 at non-integers, and undefined (some sources I've seen express it as

\infty

) at integers, I'm sure.

here is the main question but it is in persian :smile:

Reply 9

username3112014

is this true for answer?

Reply 10

username3112014

Original post by huvaxshatra

is this true for answer?

oops i used persian numbers i will edit it

Reply 11

username3112014

Original post by huvaxshatra

oops i used persian numbers i will edit it

Reply 12

math42

Original post by huvaxshatra

So I presume you are looking for the one sided limit, i.e. the left derivative? If that is the case, I believe your workings are correct, although it is rather a strange question as it seems to reduce to the derivative of |x| at 1 which we should know is 1 anyway. (and indeed the answer will be independent of a)