Lim x -3 x-4-3 x-2x-1-3

Lim_x →∞{3x 4/3x+2}^x+1/3 = lim_x →∞(1 + 3x 4 3x 2/3x + 2 )^x+1/3 = lim_x → 0(1+ 6/3x+2 )^x+1/3 = e^lim_x →∞( 6/3x+2 )(x+1/3 ) = e^lim_x →∞( 6x 6/9x+2 ) ...

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Byju's Answer

Standard XII

Mathematics

Standard Limits to Remove Indeterminate Form

lim x →∞3 x-4...

Question

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

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Solution

${lim}_{x \to \infty} {\frac{3 x - 4}{3 x + 2}}^{\frac{x + 1}{3}} = {lim}_{x \to \infty} {(\frac{1 + 3 x - 4 - 3 x - 2}{3 x + 2})}^{\frac{x + 1}{3}} = {lim}_{x \to 0} {(1 + \frac{- 6}{3 x + 2})}^{\frac{x + 1}{3}} = e^{{lim}_{x \to \infty} (\frac{- 6}{3 x + 2}) (\frac{x + 1}{3})} = e^{{lim}_{x \to \infty} (\frac{- 6 x - 6}{9 x + 2})} = e^{\frac{- 6}{9}} = e^{\frac{- 2}{3}}$

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Similar questions

lim x \to \infty {(\frac{3 x - 4}{3 x + 2})}^{\frac{x + 1}{3}}

is equal to

Solve the following:

lim x \to \infty {(\frac{3 x - 4}{3 x + 2})}^{\frac{x + 1}{3}}

lim x \to 3 \frac{\sqrt{3 x} - 3}{\sqrt{2 x - 4} - \sqrt{2}}

is equal to :

lim x \to \infty {[\frac{3 x - 4}{3 x + 2}]}^{\frac{x + 1}{3}}

Q. Arrange the following limits in the ascending order
a)

lim x \to 0 {(\frac{1^{x} + 2^{x} + 4^{x}}{3})}^{\frac{1}{x}}

lim x \to 0 {(\frac{2^{x} + 3^{x} + 8^{x} + 27^{x}}{4})}^{\frac{1}{x}}

lim x \to 0 {⎡ ⎣ \frac{1^{x} + (\frac{1}{2})^{x} + (\frac{1}{4})^{x}}{3} ⎤ ⎦}^{\frac{1}{x}}

lim x \to 0 {⎡ ⎣ \frac{(\frac{1}{2})^{x} + (\frac{1}{3})^{x} + (\frac{1}{8})^{x} + (\frac{1}{27})^{x}}{4} ⎤ ⎦}^{\frac{1}{x}}

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limx→∞{3x−43x+2}x+13

limx→∞{3x−43x+2}x+13=limx→∞(1+3x−4−3x−23x+2)x+13=limx→0(1+−63x+2)x+13=elimx→∞(−63x+2)(x+13)=elimx→∞(−6x−69x+2)=e−69=e−23

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