Mathematical expressions 1

Mathematical expressions \( x = {-b \pm \sqrt{b^2-4ac} \over 2a} \) inside text.
Mathematical expressions outside text: \[ x = {-b \pm \sqrt{b^2-4ac} \over 2a} \]

Mathematical expressions 2

Mathematical expressions \( x^2 + y^2 = z^2 \) inside text.
Mathematical expressions outside text: \[ x^2 + y^2 = z^2 \]

Sums

Sum \(\sum_{n=1}^{\infty} 2^{-n} = 1\) inside text.
Sum outside text: \[ \sum_{n=1}^{\infty} 2^{-n} = 1 \]

Products

Product \(\prod_{i=a}^{b} f(i)\) inside text.
Product outside text: \[ \prod_{i=a}^{b} f(i) \]

Limits

Limit \(\lim_{x\to\infty} f(x)\) inside text.
Limit outside text: \[ \lim_{x\to\infty} f(x) \]

Integrals

Integral \(\int_{a}^{b} x^2 \,dx\) inside text.
Integral outside text: \[ \int_{a}^{b} x^2 \,dx \]

Buses

The carbon dioxide emissions produced by buses are organized in four categories. The carbon dioxide emission produced by diesel buses is 0.10231 grammes per kilometer. The carbon dioxide emission produced by CNG buses is 0.08 grammes per kilometer. The carbon dioxide emission produced by petrol buses is 0.10231 grammes per kilometer. If the buses do not use fossil fuel, their dioxide carbon emissions are 0 grammes per kilometer.
To work out buses dioxide emissions, we use the next formula: \[CO^2 = {Cte + \sqrt{f(km)} \over t}.\]
Where:

• \(Cte\) is a constant, since the engine requires some fuel to initialize.
• \(km\) are the kilometers.
• \(f\) is a coefficient depending on the type of fuel (see paragraph above).
• \(t\) is the temperature, since in winter the engines require less fuel.

Cars

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Planes

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