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If `f(x)=root (3)(8x^(3)+mx^(2))-nx` such that `lim_(xrarroo)f(x)=1` then(A) `m+n=15`(B) `m-n=10`(C) `m-n=12`(D) `m+n=14`A. `m+n=15`B. `m-n=10`C. `m-n=12`D. `m+n=14` |
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Answer» Correct Answer - B::D `lim_(xrarroo)root(3)(8x^(3)+mx^(2))-nx` `=lim_(xrarroo)((8-n^(3))x^(3)+mx^(2))/(root(3)((8x^(3)+mx^(2))^(2))+nx^(3)sqrt(8x^(3)+mx^(2))+n^(2)x^(2))` for limit to be finite `8-n^(3)=0impliesn=2` Hence `lim_(xrarroo)f(x)=lim_(xrarroo)m/(root(3)((8+m/x)^(2))+2root(3)((8+m/x))+4)` `=m/12=1impliesm=12` |
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