# How do we know the intensity ratio of multiplets in the #""^1H# #NMR# spectrum?

Pascal's triangle gives the relative intensity of multiplets.........

....the pattern of peak intensities measured by integration follows

A singlet has relative intensity

A doublet has relative intensity

A triplet has relative intensity

A quartet has relative intensity

And a quintet has relative intensity

Notice the relationship between the triangle and the relative intensities?

Even with the best, highest field spectrometers, quintets, and hextets, and higher multiplets may TEND to overlap and lose resolution. The inset shows the methine absorption for

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The intensity ratio of multiplets in the 1H NMR spectrum is determined by the number of equivalent protons in each signal. The ratio is given by the Pascal's triangle rule, where the intensity ratio of peaks in an NMR multiplet corresponds to the coefficients of the binomial expansion of (n+1)^N, where n is the number of neighboring equivalent protons and N is the number of equivalent protons in the multiplet.

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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.

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