InterviewSolution
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InterviewSolution
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`lim_(xto0) ((e^(x)-e^(-x))/(x))` का मान ज्ञात कीजिये। |
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Answer» हम जानते है कि `e^(x)=1+x+(x^(2))/(2!)+(x^(3))/(3!)+(x^(4))/(4!)+...oo` तथा `e^(-x)=1-x+(x^(2))/(2!)-(x^(3))/(3!)+(x^(4))/(4!)...oo` `therefore e^(x)-e^(-x)=2(x+(x^(3))/(3!)+(x^(5))/(5!)+...oo)` `=2x(1+(x^(2))/(3!)+(x^(4))/(5!)+...oo)` `therefore (e^(x)-e^(-x))/(x)=2[1+(x^(2))/(3!)+(x^(4))/(5!)+...oo]` अतः `underset(xto0)lim(e^(x)-e^(-x))/(x)=underset(xto0)lim2[1+(x^(2))/(3!)+(x^(4))/(5!)+...oo]` `=2[1+0+0+...]` (सिमा लेने पर ) `=2` |
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