The calculation process is as follows:

(3n+2)/(5n+ 1)

=(3+2/n)/(5+ 1/n)

When n→∞, 2/n→ 0, 1/n → 0.

therefore

lim(n→∞)(3+2/n)/(5+ 1/n)

=(3+0)/(5+0)=3/5

Equivalent infinitesimal transformation, (can only be used in multiplication and division, does not mean that it cannot be used in addition and subtraction, but only if the limit still exists after splitting). The x power of e-1 or the a power of (1+x)-1 is equivalent to Ax, etc. (x becomes infinitesimal when it approaches infinity).

Extended data:

Equivalent infinitesimal replacement is a common method to calculate indefinite limit, which can simplify complex problems and simplify complex ones.

When seeking the limit, use the condition of equivalent infinitesimal:

The quantity to be replaced, when the limit is taken, the limit value is 0;

Substituted quantities can be replaced by equivalent infinitesimals as elements to be multiplied or divided, but not as elements to be added and subtracted.

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