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Question Number 352 by Vishal Bhardwaj last updated on 25/Jan/15

Q.  Define ••  LHD(left hand  derivative) = f(a−0)  lim_(h→0)  ((f(a−h)−f(a))/(−h))

$${Q}.\:\:{Define}\:\bullet\bullet\:\:{LHD}\left({left}\:{hand}\right. \\ $$$$\left.{derivative}\right)\:=\:{f}\left({a}−\mathrm{0}\right) \\ $$$$\underset{{h}\rightarrow\mathrm{0}} {{lim}}\:\frac{{f}\left({a}−{h}\right)−{f}\left({a}\right)}{−{h}} \\ $$$$ \\ $$$$ \\ $$

Commented by prakash jain last updated on 23/Dec/14

The question is not clear. Can you   please clarify:  LHD=lim_(h→0)  ((f(a−h)−f(a))/(−h))

$$\mathrm{The}\:\mathrm{question}\:\mathrm{is}\:\mathrm{not}\:\mathrm{clear}.\:\mathrm{Can}\:\mathrm{you}\: \\ $$$$\mathrm{please}\:\mathrm{clarify}: \\ $$$$\mathrm{LHD}=\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{f}\left({a}−{h}\right)−{f}\left({a}\right)}{−{h}} \\ $$

Answered by prakash jain last updated on 25/Dec/14

Left Hand Derivative of f(x) at x=a  is defined as  lim_(h→0) ((f(a−h)−f(a))/(−h))  The definition that you gave in the  question is correct.

$$\mathrm{Left}\:\mathrm{Hand}\:\mathrm{Derivative}\:\mathrm{of}\:{f}\left({x}\right)\:\mathrm{at}\:{x}={a} \\ $$$$\mathrm{is}\:\mathrm{defined}\:\mathrm{as} \\ $$$$\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{f}\left({a}−{h}\right)−{f}\left({a}\right)}{−{h}} \\ $$$$\mathrm{The}\:\mathrm{definition}\:\mathrm{that}\:\mathrm{you}\:\mathrm{gave}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{question}\:\mathrm{is}\:\mathrm{correct}. \\ $$

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