InterviewSolution
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InterviewSolution
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Evaluate, `lim_(xtosqrt(2)) (x^(4)-4)/(x^7(2)+3sqrt(2x)-8)`. |
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Answer» Given, `underset(xtosqrt(2))"lim"((x^(4)-4))/(x^(2)+3sqrt(2)x-8)= underset(xtosqrt(2))"lim"((x^(2))^(2)-(2)^(2))/(x^(2)+3sqrt(2)x-8)` `=underset(xtosqrt(2))"lim" ((x^(2)-2)(x^(2)+2))/(x^(2)+4sqrt(2)x-sqrt(2)x-8)` `=underset(xtosqrt(2))"lim"((x-sqrt(2))(x+sqrt(2))(x^(2)+2))/(x(x+4sqrt(2))-sqrt(2)(x+4sqrt(2)))` `=underset(xtosqrt(2))"lim"((x-sqrt(2))(x+sqrt(2))(x^(2)+2))/((x-sqrt(2))(x+4sqrt(2)))` `=underset(xtosqrt(2))"lim"((x+sqrt(2))(x^(2)+2))/((x+4sqrt(2)))` `=((sqrt(2)+sqrt(2))[(sqrt(2)^(2)+2)])/((sqrt(2)+4sqrt(2)))` `=(2sqrt(2)(2+2))/(5sqrt(2))= 8/5` |
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