Explain-the-proof-with-appropriate-diagram-Lim-h-0-f-x-f-x-h-h-dy-dx-where-y-f-x-

Question Number 75402 by vishalbhardwaj last updated on 10/Dec/19

Explain the proof

with appropriate

diagram :

{Lim}_{h \to 0} \frac{f (x) - f (x - h)}{- h}

= \frac{d y}{d x}, where y = f (x)

Commented by Kunal12588 last updated on 10/Dec/19

{i s n}^{'} t i t t h e d e f i n a t i o n o f d e r i v a t i v e ?

f i r s t p r i n c i p l e

\frac{d y}{d x} = \underset{Δ x \to 0}{l i m} \frac{Δ y}{Δ x} = \underset{Δ x \to 0}{l i m} \frac{f (x + Δ x) - f (x)}{Δ x}

Commented by vishalbhardwaj last updated on 10/Dec/19

sir this is LHD

Commented by Kunal12588 last updated on 10/Dec/19

Δ x = 0 - h

\Rightarrow Δ x = - h

Δ x \to 0 \Rightarrow h \to 0

L H D = \underset{h \to 0}{l i m} \frac{f (x - h) - f (x)}{- h}

Commented by vishalbhardwaj last updated on 12/Dec/19

please explain the proof of this

with the help of diagram