Evaluate the limit-limx-x-4x2-1-1

We have, lim_x→∞x√(4x^2+1) 1 =lim_x→∞x√(x^2 ( 4+1x^2 )) 1 =lim_x→∞xx ( √( ( 4+1x^2 )) 1x ) =lim_x→∞1 ( √( ( 4+1x^2 )) 1x ) Where x→∞, then 1x→ 0 =1(√((4+0 ...

You visited us 2 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Algebra of Limits

Evaluate the ...

Question

Evaluate the limit:
$lim x \to \infty \frac{x}{\sqrt{4 x^{2} + 1} - 1}$

Open in App

Solution

We have,
$lim x \to \infty \frac{x}{\sqrt{4 x^{2} + 1} - 1}$

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

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

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

Where $x \to \infty$ , then $\frac{1}{x} \to 0$

$= \frac{1}{(\sqrt{(4 + 0)} - 0)}$

$= \frac{1}{\sqrt{4}} = \frac{1}{2}$

Suggest Corrections

Similar questions

Q. Evaluate the limit:

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

Q. Evaluate the limit:

lim x \to 4 \frac{x^{2} - 16}{\sqrt{x} - 2}

Q. Evaluate the limit:

lim x \to \infty \frac{3 x^{3} - 4 x^{2} + 6 x - 1}{2 x^{3} + x^{2} - 5 x + 7}

Q. Evaluate the limit:

lim x \to - \infty (\sqrt{4 x^{2} - 7 x} + 2 x)

Q. Evaluate the limit:

lim x \to 0 \frac{\sqrt{1 + x} - 1}{x}

Join BYJU'S Learning Program

Explore more

Algebra of Limits

Standard XII Mathematics

Join BYJU'S Learning Program

Evaluate the limit: limx→∞x√4x2+1−1

We have, limx→∞x√4x2+1−1 =limx→∞x√x2(4+1x2)−1 =limx→∞xx(√(4+1x2)−1x) =limx→∞1(√(4+1x2)−1x) Where x→∞, then 1x→0 =1(√(4+0)−0) =1√4=12

Evaluate the limit:
$lim x \to \infty \frac{x}{\sqrt{4 x^{2} + 1} - 1}$