Recent content by klarka

Homework Statement g(x) = 1 if x is rational, 0 if x is irrational. Determine the limit, or prove it doesn't exist. lim g(x)sinx x->0 Homework Equations The Attempt at a Solution I said the limit is 0. 0 < |g(x)sinx| < |sinx| lim |g(x)sinx|= 0 x->0 -|sinx| < g(x)sinx < sinx lim...

Homework Statement Prove that \frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+...+\frac{1}{\sqrt{n}}\geq\sqrt{n} for all n \in N Homework Equations The Attempt at a Solution p(1): \frac{1}{\sqrt{1}} = \frac{1}{1} = 1 = \sqrt{1} \geq \sqrt{1} Let \frac{1}{\sqrt{1}} + \frac{1}{\sqrt{2}} +...+...