Evaluation of the Form $$1^\infty$$

Rarely Tested

Evaluation of the Form $$1^\infty$$

If:

$$\lim_{x\to a}f(x)=1$$

and:

$$\lim_{x\to a}g(x)=\infty$$

then:

$$\lim_{x\to a}f(x)^{g(x)}=\lim_{x\to a}e^{g(x)\ln f(x)}$$

Usage

- Used to transform the indeterminate form $$1^\infty$$ into an exponential limit.

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