What are alkyl, aryl, aliphatic and aromatic groups?
They are different types of organic side groups.
- Alkyl
#-# a side group consisting of carbon and hydrogen atoms only, eg.,#"CH"_3, "C"_2"H"_5# etc. - Aryl
#-# a side group consisting of an aromatic ring, usually benzene, eg.,#"C"_6"H"_5"C"_2"H"_5"OH"# - Aliphatic - any side group that doesn't have an aromatic ring in it
- Aromatic - a side group which is the same as an aryl side group
#-# although some sources state that an aromatic group is derived only from benzene whilst an aryl group comes from any univalent organic radical.
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Alkyl groups are groups of atoms derived from alkanes by removing one hydrogen atom. Aryl groups are derived from aromatic compounds by removing one hydrogen atom. Aliphatic compounds are compounds containing carbon and hydrogen joined together in straight chains, branched chains, or non-aromatic rings. Aromatic compounds are cyclic, planar molecules with delocalized pi electrons, giving them stability.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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