lim_x → 22x+58 x^3 =2(2)+58 (2)^3=5+48 8=90=∞ Apply L Hospital Rule I lim_x → 2 #160; =2x+58 x^3=lim_x → 2(2x+5)^1(8 x^3)^1 lim ...

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Existence of Limit

lim x→ 2 2x+5...

Question

$lim x \to 2 \frac{2 x + 5}{8 - x^{3}}$

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Solution

$lim x \to 2 \frac{2 x + 5}{8 - x^{3}}$

$= \frac{2 (2) + 5}{8 - (2)^{3}} = \frac{5 + 4}{8 - 8} = \frac{9}{0} = \infty$
Apply $L -$ Hospital Rule $- I$

$lim x \to 2 = \frac{2 x + 5}{8 - x^{3}} = lim x \to 2 \frac{(2 x + 5)^{1}}{(8 - x^{3})^{1}}$

$lim x \to 2 \frac{2}{- 3 x^{2}}$

$= \frac{2}{- 3 (2)^{2}} = \frac{- 2}{12}$

$= - 1 / 6$

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