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Excuse me, when the limit of x approaches infinity, is it e?
When (x→∞) lim (1+1/x) x = limexln (1+1/x)

because

X→∞, so 1\x→0. Ln (1+1/x) =1\ x is replaced by equivalent infinitesimal.

So the original formula becomes

When (x→∞)

lim( 1+ 1/x)^x=lime^xln( 1+ 1/x)=lime^x* 1/x=e

Equivalent formula at limit:

1、e^x- 1~x (x→0)

2、e^(x^2)- 1~x^2 (x→0)

3、 1-cosx~ 1/2x^2 (x→0)

4、 1-cos(x^2)~ 1/2x^4(x→0)

5、sinx~x (x→0)

6、tanx~x (x→0)

7、arcsinx~x (x→0)

8. Arctangent x~x (x→0)

9、 1-cosx~ 1/2x^2 (x→0)

10、a^x- 1~xlna (x→0)

1 1、e^x- 1~x (x→0)

12、ln( 1+x)~x (x→0)

13、( 1+Bx)^a- 1~aBx (x→0)

14、[( 1+x)^ 1/n]- 1~ 1/nx(x→0)

15、loga( 1+x)~x/lna(x→0)