CBSE Class 11-science Answered

Asked by Renuka Ganesh | 20 May, 2014, 01:02: PM

Expert Answer

$f open parentheses x close parentheses equals open curly brackets table attributes columnalign left end attributes row cell x squared open vertical bar cos straight pi over x close vertical bar space space comma space x not equal to 0 end cell row cell 0 space space space space space space space space space space space space space space space space space x equals 0 space space space space space space space space end cell end table close L. H. D equals limit as h rightwards arrow 0 to the power of minus of fraction numerator open parentheses minus h close parentheses squared open vertical bar cos fraction numerator straight pi over denominator minus h end fraction close vertical bar over denominator minus h end fraction space space space space space space space space space space equals space limit as h rightwards arrow 0 to the power of minus of h open vertical bar cos straight pi over h close vertical bar space space space space space space space space space space equals space 0 space cross times space f i n i t e space v a l u e equals space 0 R. H. D equals limit as h rightwards arrow 0 to the power of plus of fraction numerator open parentheses h close parentheses squared open vertical bar cos straight pi over h close vertical bar over denominator h end fraction space space space space space space space space space space equals space limit as h rightwards arrow 0 to the power of plus of h open vertical bar cos straight pi over h close vertical bar space space space space space space space space space space equals space 0 space cross times space f i n i t e space v a l u e equals space 0 f o r space x space equals space 2 L. H. D equals limit as h rightwards arrow 0 to the power of minus of fraction numerator open parentheses 2 minus h close parentheses squared open vertical bar cos fraction numerator straight pi over denominator 2 minus h end fraction close vertical bar over denominator 2 minus h end fraction space space space space space space space space space space equals space limit as h rightwards arrow 0 to the power of minus of open parentheses 2 minus h close parentheses open vertical bar cos fraction numerator straight pi over denominator 2 minus h end fraction close vertical bar space space space space space space space space space space equals space 2 space cross times space 0 space equals space 0 R. H. D equals limit as h rightwards arrow 0 to the power of plus of fraction numerator open parentheses 2 plus h close parentheses squared open vertical bar cos fraction numerator straight pi over denominator 2 plus h end fraction close vertical bar over denominator 2 plus h end fraction space space space space space space space space space space equals space stack lim open parentheses 2 plus h close parentheses with h rightwards arrow 0 to the power of plus below open vertical bar cos fraction numerator straight pi over denominator 2 plus h end fraction close vertical bar space space space space space space space space space space equals 2 cross times 0 equals space 0 T h u s comma space t h e space g i v e n space f u n c t i o n space i s space d i f f e r e n t i a b l e space a t space x space equals space 0 space a n d space x space equals space 2$