Can we use the Equivalent Infinitesimal Substitution when the limit is exponentially calculated? For example, Lim [x - > 0, (1 + SiNx) ^ (1 / 2x)], can X in index 1 / 2x be directly replaced by SiNx? Can't SiNx be directly replaced by X? | Math enthusiast | Mathematical art

Can we use the Equivalent Infinitesimal Substitution when the limit is exponentially calculated? For example, Lim [x - > 0, (1 + SiNx) ^ (1 / 2x)], can X in index 1 / 2x be directly replaced by SiNx? Can't SiNx be directly replaced by X?

It depends on your understanding of the concept of equivalent infinitesimal. In fact, the concept of equivalent infinitesimal is introduced for the convenience of solving the limit according to Taylor expansion, which is only a low order approximation of Taylor expansion

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