lim_x→∞2x^2+x+5x^2+x 2 , #160; #160; #160; ( ∞∞ form ) Put x=1y lim_y→ 02+y+5y^21+y 2y^2=2 ...

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Existence of Limit

limx→∞2x2+x+5...

Question

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

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Solution

$lim x \to \infty \frac{2 x^{2} + x + 5}{x^{2} + x - 2}$ , $(\frac{\infty}{\infty} f o r m)$

Put $x = \frac{1}{y}$

$lim y \to 0 \frac{2 + y + 5 y^{2}}{1 + y - 2 y^{2}} = 2$

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