Evaluate
\frac{x^{2}}{2}-4
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\frac{x^{2}}{2}-4
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\left(\frac{1}{2}x\right)^{2}-4-\left(-\frac{1}{4}x^{2}\right)
Consider \left(\frac{1}{2}x-2\right)\left(\frac{1}{2}x+2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.
\left(\frac{1}{2}\right)^{2}x^{2}-4-\left(-\frac{1}{4}x^{2}\right)
Expand \left(\frac{1}{2}x\right)^{2}.
\frac{1}{4}x^{2}-4-\left(-\frac{1}{4}x^{2}\right)
Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.
\frac{1}{4}x^{2}-4+\frac{1}{4}x^{2}
The opposite of -\frac{1}{4}x^{2} is \frac{1}{4}x^{2}.
\frac{1}{2}x^{2}-4
Combine \frac{1}{4}x^{2} and \frac{1}{4}x^{2} to get \frac{1}{2}x^{2}.
\left(\frac{1}{2}x\right)^{2}-4-\left(-\frac{1}{4}x^{2}\right)
Consider \left(\frac{1}{2}x-2\right)\left(\frac{1}{2}x+2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.
\left(\frac{1}{2}\right)^{2}x^{2}-4-\left(-\frac{1}{4}x^{2}\right)
Expand \left(\frac{1}{2}x\right)^{2}.
\frac{1}{4}x^{2}-4-\left(-\frac{1}{4}x^{2}\right)
Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.
\frac{1}{4}x^{2}-4+\frac{1}{4}x^{2}
The opposite of -\frac{1}{4}x^{2} is \frac{1}{4}x^{2}.
\frac{1}{2}x^{2}-4
Combine \frac{1}{4}x^{2} and \frac{1}{4}x^{2} to get \frac{1}{2}x^{2}.
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Simultaneous equation
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Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
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