Lim x -5 x3-6 x-9-4 x6

=lim_x →∞5x^3 6x/√(9+4x^6)=lim_x →∞x^3 ( 5 6x/x^3 )/√(x^6 ( 9/x^6+4 )) =lim_x →∞x^3 ( 5 6x/x^2 )/x^3 √(9/x^6+4) =lim_x →∞ 5 6x/x^2/√(9/x^6+4) as x→∞ ,1/x→ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

L'Hospital Rule to Remove Indeterminate Form

lim x →∞5 x3-...

Question

${lim}_{x \to \infty} \frac{5 x^{3} - 6 x}{\sqrt{9 + 4 x^{6}}}$

Open in App

Solution

$= {lim}_{x \to \infty} \frac{5 x^{3} - 6 x}{\sqrt{9 + 4 x^{6}}} = {lim}_{x \to \infty} \frac{x^{3} (5 - \frac{6 x}{x^{3}})}{\sqrt{x^{6} (\frac{9}{x^{6}} + 4)}}$

$= {lim}_{x \to \infty} \frac{x^{3} (5 - \frac{6 x}{x^{2}})}{x^{3} \sqrt{\frac{9}{x^{6}} + 4}}$

$= {lim}_{x \to \infty} \frac{5 - \frac{6 x}{x^{2}}}{\sqrt{\frac{9}{x^{6}} + 4}}$

$a s x \to \infty, \frac{1}{x} \to 0$

$= \frac{5}{\sqrt{4}} = \frac{5}{2}$

Suggest Corrections

Similar questions

Q. Evaluate the limit to infinity

lim x \to \infty \frac{{5 x}^{3} - 6}{\sqrt{9 + 4 x^{6}}} = \frac{5}{2}

Q. Solve

lim x \to 3 \frac{x^{3} - 7 x^{2} + 15 x - 9}{x^{4} - 5 x^{3} + 27 x - 27}

lim x \to 3 \frac{x^{3} - 7 x^{2} + 15 x - 9}{x^{4} - 5 x^{3} + 27 x - 27}

is equal to

Q. Evaluate the following limits

lim x \to 3 \frac{x^{2} - 9}{x^{2} (x^{2} - 6 x + 9)}

\lim_{x \to \infty} \frac{5 x^{3} - 6}{\sqrt{9 + 4 x^{6}}}

Join BYJU'S Learning Program

limx→∞5x3−6x√9+4x6

=limx→∞5x3−6x√9+4x6=limx→∞x3(5−6xx3)√x6(9x6+4) =limx→∞x3(5−6xx2)x3√9x6+4 =limx→∞5−6xx2√9x6+4 as x→∞,1x→0 =5√4=52

${lim}_{x \to \infty} \frac{5 x^{3} - 6 x}{\sqrt{9 + 4 x^{6}}}$