Lim x - x 2-2 x-32 x 2-x-53 x-23 x-2

Limx #8594; #8734; #160;x2+2x+32x2+x+53x 23x+2=limx #8594; #8734; #160;1+x2+2x+32x2+x+5 13x 23x+2=limx #8594; #8734; #160;1+x2+2x+3 2x2+x+52x2 ...

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Existence of Limit

lim x →∞ x 2+...

Question

$\lim_{x \to \infty} {\{\frac{x^{2} + 2 x + 3}{2 x^{2} + x + 5}\}}^{\frac{3 x - 2}{3 x + 2}}$

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Solution

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

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

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$(i) {lim}_{x \to 2^{+}} \frac{x - 3}{x^{2} - 4}$

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$(i i i) {lim}_{x \to 0^{+}} \frac{1}{3 x}$

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$(v i) {lim}_{x \to \frac{π^{-}}{2}} t a n x$

$(v i i) {lim}_{x \to \frac{π}{2^{+}}} s e c x$

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$(i x) {lim}_{x \to - 2^{+}} \frac{x^{2} - 1}{2 x + 4}$

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