f-x-d-dx-f-x- – Tinku Tara

Question Number 131206 by Study last updated on 02/Feb/21

f (x) = \infty

\frac{d}{d x} f (x) = ?

Commented by mr W last updated on 02/Feb/21

\infty i s n o t a v a r i a b l e, i s n o t a c o n s t a n t .

f (x) = \infty h a s n o m e a n i n g!

\lim_{x \to a} f (x) = \infty h a s m e a n i n g .

Commented by JDamian last updated on 02/Feb/21

\infty i s n o t a r e a l n u m b e r

\infty \notin ℜ

Commented by mr W last updated on 02/Feb/21

\infty i s n o t a n u m b e r a t a l l!

Commented by MJS_new last updated on 03/Feb/21

I still believe that if f (x) = [t e r m w i t h o u t x]

\Rightarrow \frac{d}{d x} [f (x)] = 0

example :

f (x) = \frac{1}{r}; r \in R \Rightarrow \frac{d}{d x} [f (x)] = 0

we have the limit

f^{'} (p) = \lim_{h \to 0} \frac{f (p + h) - f (p - h)}{2 h}

in this case

f^{'} (p) = \lim_{h \to 0} \lim_{r \to 0} \frac{\frac{1}{r} - \frac{1}{r}}{2 h} =

= \lim_{h \to 0} \lim_{r \to 0} \frac{0}{2 h} = 0

if I^{'} m wrong please prove

Commented by mr W last updated on 03/Feb/21

y e s, f (x) {m u s n}^{'} t h a v e t e r m w i t h x, b u t

i t m u s t b e v a l i d l y d e f i n e d a n d

r e p r e s e n t v a l u e s .

Answered by prakash jain last updated on 03/Feb/21

\frac{d}{d x} (\infty) = 0