Solved: Indeterminate Forms Show that the indeterminate forms and do not always have a
Chapter 8, Problem 111(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) \(\lim _{x \rightarrow \infinity} x^{\ln 2 /(1+\ln x)}\)
(c) \(\lim _{x \rightarrow 0}(x+1)^{(\ln 2) / x}\)
Text Transcription:
0^0, infinity^0, and 1^infinity
lim_x rightarrow 0^+ x^ln 2/(1+ln x)
lim_x rightarrow infinity x^ln 2/(1+ln x)
lim_x rightarrow 0 (x+1)^(ln 2)/x
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