Special forms and miscellaneous limitsMedium
Least Natural Value for Limit Inequality
Let [t] be the greatest integer less than or equal to t. Then the least value of 
for which
![\mathop {\lim }\limits_{x \to {0^ + }} \left( {x\left( {\left[ {\frac{1}{x}} \right] + \left[ {\frac{2}{x}} \right] + ..... + \left[ {\frac{p}{x}} \right]} \right)-{x^2}\left( {\left[ {\frac{1}{{{x^2}}}} \right] + \left[ {\frac{{{2^2}}}{{{x^2}}}} \right] + .... + \left[ {\frac{{{9^2}}}{{{x^2}}}} \right]} \right)} \right) \geqslant 1](https://d2lbh14zkcqlst.cloudfront.net/content_data/content_images/17397833621018997229.png)
is equal to ____.
for whichis equal to ____.
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