Consider the geometric progression
 
Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '.
 
By considering the limit as Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '., deduce expressions for  f'(p) in the cases
 
(i) f(x) = Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '.,           (ii) f(x) =Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '. , for all positive integers Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '.
 
Answer:
              (i) Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '.
              (ii) Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '.

Asked by Sreedhar Rao | 23rd 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

Answered by Avinash Soni | 26th May, 2014, 03:22: PM

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