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If |f(x)|lex^(2), then prove that lim(xt...

If `|f(x)|lex^(2),` then prove that `lim_(xto0) (f(x))/(x)=0.`

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Verified by Experts

We have `|f(x)|lex^(2)`
`:." "|(f(x))/(x)|le|x|`
`implies" "underset(xto0)lim|(f(x))/(x)|leunderset(xto0)lim|x|`
`implies" "|underset(xto0)lim(f(x))/(x)|le0`
`implies" "|underset(xto0)lim(f(x))/(x)|=0`
`implies" "underset(xto0)lim(f(x))/(x)=0`
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