If a and b are positive and [x] denotes greatest integer less than or equal to x, then find `lim_(xto0^(+)) x/a[(b)/(x)].`
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`L=underset(xto0^(+))limx/a[(b)/(x)].` `=underset(xto0^(+))limx/a(b/x-{b/x})," "`where `{.}` represents the functional part function `=underset(xto0^(+))lim(b/a-x/a{b/x})` `=b/a-1/aunderset(xto0^(+))lim({b/x}}/(1/x)` Since `0lt{b/x}lt1 " and "underset(xto0^(+))lim1/x=oo,` we have `L= b/a-0=b/a`
LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS
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