Question

Lim of (1 + x)ˣ as x→[infinity].
A. 0
B. 1
C. e
D. [infinity]

Answer 1

The limit of (1 + x)^x as x approaches infinity is infinity, since the base (1+x) grows faster than the power x can diminish it.

Step-by-step explanation:

The limit of (1 + x)^x as x approaches infinity is a well-known result in mathematics related to the number e, which is approximately 2.71828.

This expression does not converge to a finite number as x grows larger; instead, it grows without bound and thus the limit is infinity, option D. The function (1 + x)^x becomes very large because the base (1+x) grows faster than the diminution caused by the power of x.