CBSE Class 11-science Answered

Consider the geometric progression

By considering the limit as , deduce expressions for f'(p) in the cases

(i) f(x) = ,           (ii) f(x) = , for all positive integers

Answer:

              (i)

              (ii)

Asked by Sreedhar Rao | 23 May, 2014, 06:58: AM

Expert Answer

$f open parentheses q close parentheses equals q to the power of n minus 1 end exponent space plus space q to the power of n minus 2 end exponent space plus space q to the power of n minus 3 end exponent p squared plus space......... plus space q p to the power of n minus 2 end exponent space plus space p to the power of n minus 1 end exponent f open parentheses q close parentheses equals q to the power of n minus 1 end exponent fraction numerator open square brackets open parentheses begin display style p over q end style close parentheses to the power of n minus 1 close square brackets over denominator begin display style p over q end style minus 1 end fraction equals fraction numerator p to the power of n minus q to the power of n over denominator p minus q end fraction limit as q rightwards arrow p of fraction numerator p to the power of n minus q to the power of n over denominator p minus q end fraction equals n p to the power of n minus 1 end exponent left parenthesis i right parenthesis space f open parentheses x close parentheses equals x to the power of n rightwards double arrow f apostrophe open parentheses x close parentheses equals n x to the power of n minus 1 end exponent rightwards double arrow f apostrophe open parentheses p close parentheses equals n p to the power of n minus 1 end exponent left parenthesis i i right parenthesis space f open parentheses x close parentheses equals x to the power of minus n end exponent rightwards double arrow f apostrophe open parentheses x close parentheses equals minus n x to the power of minus open parentheses n plus 1 close parentheses end exponent rightwards double arrow f apostrophe open parentheses p close parentheses equals minus n p to the power of minus open parentheses n plus 1 close parentheses end exponent$