Lösung 2.3:7c

Aus Online Mathematik Brückenkurs 1

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If we complete the square
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<math>x^{2}+x+1=\left( x+\frac{1}{2} \right)^{2}-\left( \frac{1}{2} \right)^{2}+1=\left( x+\frac{1}{2} \right)^{2}+\frac{3}{4}</math>
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we see on the right-hand side that we can make the expression arbitrarily large simply by choosing
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<math>x+\frac{1}{2}</math>
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sufficiently large. Hence, there is no maximum value.

Version vom 11:18, 21. Sep. 2008

If we complete the square


\displaystyle x^{2}+x+1=\left( x+\frac{1}{2} \right)^{2}-\left( \frac{1}{2} \right)^{2}+1=\left( x+\frac{1}{2} \right)^{2}+\frac{3}{4}


we see on the right-hand side that we can make the expression arbitrarily large simply by choosing \displaystyle x+\frac{1}{2} sufficiently large. Hence, there is no maximum value.

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_2.3:7c“