Show that the indeterminate forms and do not always have a value of 1 by evaluating each
Chapter 8, Problem 119(choose chapter or problem)
Indeterminate Forms Show that the indeterminate forms \(0^{0}\), \(\infty^{0}, \text { and } 1^{\infty}\) do not always have a value of 1 by evaluating each limit.
(a) \(\lim _{x \rightarrow 0^{+}} x^{\ln 2 /(1+\ln x)}\)
(b) \(\lim _{x \rightarrow \infty} x^{\ln 2 /(1+\ln x)}\)
(c) \(\lim _{x \rightarrow 0}(x+1)^{(\ln 2) / x}\)
Text Transcription:
0^0
infty^0
1^infty
lim _x rightarrow 0^+x^ln 2 1+\ln x
lim _x rightarrow infty x^ln 2 1+ln x
lim _x rightarrow 0 x+1^ln 2 x
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