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InterviewSolution
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Statement -1: If a and b are positive real numbers and [.] denotes the greatest integer function , then |
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Answer» Statement -1 is true, Statement-2 is true,, Statement-2 is a CORRECT explanation for Statement-1. ` 0le {x}LT 1` `rArr 0le ({x})/(x) lt (1)/(x) " for all " x gt 0 rArr lim_(XTO oo) ({x})/(x)=0` Hence, statement -2 is true. Now, `lim_(xto0^+)(x)/(a) [(b)/(a)]=lim_(xto0 ^+)(x)/(a)((b)/(x)-{(b)/(x)})=lim_(xto0^+) ((b)/(a)-(x)/(a){(b)/(x)})` ` rArr lim_(xto 0^+)(x)/(a) [(b)/(x)]=(b)/(a)-(b)/(a)lim_(xto0^+)(x)/(b) {(b)/(x)}=(b)/(a)-(b)/(a)lim_(xto0^+)({(b)/(x)})/((b)/(x))` ` rArr lim_(xto 0^+)(x)/(a) [(b)/(x)]=(b)/(a)-(b)/(a)lim_(XTOOO) ({y})/(y)," where "y=(b)/(x)` ` rArr lim_(xto 0^+)(x)/(a) [(b)/(x)]=(b)/(a)-(b)/(a)xx0=(b)/(a)""["USING statements -2"]` |
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