document.write( "Question 637748: Find limit ((x+1)^2-1)/ x
\n" ); document.write( " x->0 \n" ); document.write( "

Algebra.Com's Answer #401856 by DrBeeee(684) $\"\"$ $\"About$

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Simplify the numerator
\n" ); document.write( "[(x+1)^2-1] = x^2 + 2x +1 -1 = x^2 + 2x = [x(x+2)]
\n" ); document.write( "Rewrite the given expression
\n" ); document.write( "[(x+1)^2-1]/x = [x(x+2)]/x = [x+2]
\n" ); document.write( "Limit as x goes to 0 of [x+2] = 0+2 = 2
\n" ); document.write( "Because the numerator had a factor x, it cancelled with x in the denominator prior to x reaching a limit of 0. Thus we never did divide by zero and the answer is a finite value of 2. \n" ); document.write( "

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