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Q-Define-LHD-left-hand-derivative-f-a-0-lim-h-0-f-a-h-f-a-h-

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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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