document.write( "Question 1046280: Prove the statement using the ε, δ definition of a limit.\r
\n" ); document.write( "\n" ); document.write( "lim x^2=0
\n" ); document.write( "x→0
\n" ); document.write( "Given ε > 0, we need δ > 0 such that if 0 < |x − 0| < δ, then |x2 − 0| < ε⇔ ____________ < ε ⇔
\n" ); document.write( "|x| < _____________. Take δ = ____________.Then 0 < |x − 0| < δ right double arrow implies
\n" ); document.write( " |x2 − 0| < ε. Thus,
\n" ); document.write( "lim
\n" ); document.write( "x→0 x^2 = 0 by the definition of a limit. \n" ); document.write( "

Algebra.Com's Answer #661868 by robertb(5830) $\"\"$ $\"About$

You can put this solution on YOUR website!
1st blank: $\"abs%28x%5E2%29\"$ , or $\"abs%28x%29%5E2\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "2nd blank: $\"sqrt%28epsilon%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "3rd blank: $\"sqrt%28epsilon%29\"$ \n" ); document.write( "

\n" );