document.write( "Question 987100: Evaluate the limit, if it exisit \r
\n" ); document.write( "\n" ); document.write( "lim goes to 0 of sqrt(1+t)-sqrt(1-t)/t \n" ); document.write( "

Algebra.Com's Answer #607874 by ikleyn(52816) $\"\"$ $\"About$

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\n" ); document.write( "When t goes to 0, the function $\"sqrt%281%2Bt%29-1\"$ is equivalent to $\"1%2F2\"$ $\"t\"$ and the function $\"sqrt%281-t%29-1\"$ is equivalent to $\"-1%2F2\"$ $\"t\"$ , \r
\n" ); document.write( "\n" ); document.write( "so the difference $\"sqrt%281%2Bt%29\"$ - $\"sqrt%281-t%29\"$ is equivalent to \r
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\n" ); document.write( "\n" ); document.write( " $\"1%2F2\"$ $\"t%29\"$ - (- $\"1%2F2\"$ $\"t\"$ ) = $\"t\"$ . \r
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\n" ); document.write( "\n" ); document.write( "Therefore, the limit of $\"%28sqrt%281%2Bt%29+-+sqrt%281-t%29%29%2Ft\"$ at t -->0 is 1. \r
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