Lim x -3 x2-1-4 x2-133-1-x

Lim_x →∞{3x^2 + 1/4x^2 1}^x^3/1+x = lim_x →∞{ 1 + x^2 + 2/4x^2 1}^x^3/1+x = e^lim_x →∞{( x^2 + 2/4x^2 1 ) (x^3/1+x ) } = e^lim_x →∞{( x^5 + 2x^3/4x^2 1 ...

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Byju's Answer

Standard XII

Mathematics

Standard Limits to Remove Indeterminate Form

lim x →∞3 x2+...

Question

${lim}_{x \to \infty} {\frac{3 x^{2} + 1}{4 x^{2} - 1}}^{\frac{x^{3}}{1 + x}}$

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Solution

${lim}_{x \to \infty} {\frac{3 x^{2} + 1}{4 x^{2} - 1}}^{\frac{x^{3}}{1 + x}} = {lim}_{x \to \infty} {1 + \frac{- x^{2} + 2}{4 x^{2} - 1}}^{\frac{x^{3}}{1 + x}} = e^{{lim}_{x \to \infty} {(\frac{- x^{2} + 2}{4 x^{2} - 1}) (\frac{x^{3}}{1 + x})}} = e^{{lim}_{x \to \infty} {(\frac{- x^{5} + 2 x^{3}}{4 x^{2} - 1 + 4 x^{3} - x})}} = e^{- \infty} = 0$

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limx→∞{3x2+14x2−1}x31+x

limx→∞{3x2+14x2−1}x31+x=limx→∞{1+−x2+24x2−1}x31+x=elimx→∞{(−x2+24x2−1)(x31+x)}=elimx→∞{(−x5+2x34x2−1+4x3−x)}=e−∞=0

${lim}_{x \to \infty} {\frac{3 x^{2} + 1}{4 x^{2} - 1}}^{\frac{x^{3}}{1 + x}}$