\(\lim_{x\rightarrow\infty}f(x)^{g(x)}=\lim_{x\rightarrow\infty}f(x)^{\lim_{x\rightarrow\infty}g(x)}\)

\(\lim_{x\rightarrow\infty}f(x)^{g(x)}=\lim_{x\rightarrow\infty}f(x)^{\lim_{x\rightarrow\infty}g(x)}\)

(a) True

(b) False

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The origin of the question is Indeterminate Forms in section Differential Calculus of Engineering Mathematics

\(\lim_{x\rightarrow\infty}f(x)^{g(x)}=\lim_{x\rightarrow\infty}f(x)^{\lim_{x\rightarrow\infty}g(x)}\)

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