(1) lim_(x→0) ((5 (x)^(1/3) −3 (x)^(1/4) −(x)^(1/6) )/(4 (x)^(1/3) −(x)^(1/(24)) )) ? (2) lim_(x→∞) ((5 (x)^(1/3) −3 (x)^(1/4) −(x)^(1/6) )/(4 (x)^(1/3) − (x)^(1/(24)) )) ?


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Question Number 125056 by benjo_mathlover last updated on 08/Dec/20

$(1) \lim_{x \to 0} \frac{5 \sqrt[3]{x} - 3 \sqrt[4]{x} - \sqrt[6]{x}}{4 \sqrt[3]{x} - \sqrt[24]{x}} ?$ $(2) \lim_{x \to \infty} \frac{5 \sqrt[3]{x} - 3 \sqrt[4]{x} - \sqrt[6]{x}}{4 \sqrt[3]{x} - \sqrt[24]{x}} ?$
	Answered by bramlexs22 last updated on 08/Dec/20

	$(1) l e t x = t^{24}$ $\lim_{t \to 0} \frac{5 t^{8} - 3 t^{6} - t^{4}}{4 t^{8} - t} = \lim_{t \to 0} \frac{5 t^{7} - 3 t^{5} - t^{3}}{4 t^{7} - 1} = 0$
	Commented by bramlexs22 last updated on 08/Dec/20

	$(2) \lim_{t \to \infty} \frac{t^{8} (5 - \frac{3}{t^{2}} - \frac{1}{t^{4}})}{t^{8} (4 - \frac{1}{t^{7}})} = \frac{5}{4}$
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