document.write( "Question 637084: need your help with this function :\r
\n" ); document.write( "\n" ); document.write( "piecewise function:\r
\n" ); document.write( "\n" ); document.write( "------------x^2 – 4 if x < 3
\n" ); document.write( "g(x) =
\n" ); document.write( "------------2x – 1 if x > 3\r
\n" ); document.write( "\n" ); document.write( "The limit of the function g as x approaches 3 is as follows:\r
\n" ); document.write( "\n" ); document.write( "Thanks in advance \n" ); document.write( "
Algebra.Com's Answer #401601 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
The limit exists only if g(x) approaches the same number as x approaches 3 from both sides (right/above and left/below). Since g(x) has different formulas for x's that are above 3 and x's that are below 3 we will need to find two limits and then see if they are same number.

\n" ); document.write( "Note: Algebra.com's formula-drawing software does not \"do\" left and right so just use English:
\n" ); document.write( "The limit of \"x%5E4-4\" as x approaches 3 from the left (below) = \"%283%29%5E2-4+=+9-4+=+5\"
\n" ); document.write( "The limit of \"2x-1\" as x approaches 3 from the right (above) = \"2%283%29-1+=+6-1+=+5\"
\n" ); document.write( "As we can see, the two limits are the same. So the limit exists and it is 5:
\n" ); document.write( "\"lim%28x-%3E3%2C+g%28x%29%29+=+5\"

\n" ); document.write( "If the two limits had not been the same then \"lim%28x-%3E3%2C+g%28x%29%29\" would not exist.
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