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Home / Doubts and Solutions/KERALA/Class 11 Science/Mathematics

Find the derivation of x^2+x+1 from 1st principle.

Asked by Deebu 28th December 2014, 12:05 AM
Answered by Expert
Answer:
C o n s i d e r space y equals x squared plus x plus 1 rightwards double arrow f open parentheses x close parentheses equals x squared plus x plus 1 rightwards double arrow f open parentheses x plus h close parentheses equals open parentheses x plus h close parentheses squared plus open parentheses x plus h close parentheses plus 1 rightwards double arrow f open parentheses x plus h close parentheses equals x squared plus h squared plus 2 x h plus x plus h plus 1 W e space n o w space n e e d space t o space f i n d : fraction numerator d y over denominator d x end fraction equals limit as h rightwards arrow 0 of fraction numerator f open parentheses x plus h close parentheses minus f open parentheses x close parentheses over denominator h end fraction space space space space space space equals limit as h rightwards arrow 0 of fraction numerator x squared plus h squared plus 2 x h plus x plus h plus 1 minus x squared minus x minus 1 over denominator h end fraction space space space space space space equals limit as h rightwards arrow 0 of fraction numerator h squared plus 2 x h plus h over denominator h end fraction space space space space space space equals limit as h rightwards arrow 0 of open parentheses h plus 2 x plus 1 close parentheses space space space space space space equals limit as h rightwards arrow 0 of h plus limit as h rightwards arrow 0 of open parentheses 2 x close parentheses plus limit as h rightwards arrow 0 of open parentheses 1 close parentheses space space space space space space equals 0 plus 2 x plus 1 space space space space space space equals 2 x plus 1
Answered by Expert 28th December 2014, 7:31 PM
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