Lim x - 03 x2-2-7 x2-21 - x2 is equal to-A- eB- 1- e 2C- 1- eD - e 2

Let L = lim_x → 0 ( 3x^2 + 27x^2 + 2 )^1/x^2 [Indeterminate form 1^∞] ∴ L = e^lim_x → 01x^2 ( 3x^2 + 27x^2 + 2 1 ) = e^lim_x → 01x^2 ( 4x^27x^2+2 ) = 1e^2 ...

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

Byju's Answer

Standard XII

Mathematics

Indeterminate Forms

lim x → 03 x2...

Question

$lim x \to 0 {(\frac{3 x^{2} + 2}{7 x^{2} + 2})}^{1 / x^{2}}$ is equal to:

e

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{1}{e^{2}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{1}{e}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

e^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\frac{1}{e^{2}}$
Let $L = lim x \to 0 {(\frac{3 x^{2} + 2}{7 x^{2} + 2})}^{1 / x^{2}} [Indeterminate form 1^{\infty}]$
$∴ L = e^{lim x \to 0} \frac{1}{x^{2}} (\frac{3 x^{2} + 2}{7 x^{2} + 2} - 1)$
$= e^{lim x \to 0} \frac{1}{x^{2}} (\frac{- 4 x^{2}}{7 x^{2} + 2})$
$= \frac{1}{e^{2}}$

Suggest Corrections

Similar questions

lim x \to 0 {(\frac{3 x^{2} + 2}{7 x^{2} + 2})}^{1 / x^{2}}

is equal to:

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

= ______

Q. If

f (x) = {\begin{matrix} (1 + 2 x)^{\frac{1}{x}}, & f o r x \neq 0, e^{2} & f o r x = 0 \end{matrix}

, then

Q. Difference between the greatest and the least values of the function

f (x) = x (ln x - 2)

[1, e^{2}]

Let $f : R \to R$ be such that $f (1) = 3$ and $f^{'} (1) = 6,$ Then ${lim}_{x \to 0} {(\frac{f (1 + x)}{f (1)})}^{\frac{1}{x}}$ is equal to

Join BYJU'S Learning Program

limx→0(3x2+27x2+2)1/x2 is equal to:

The correct option is B 1e2Let L=limx→0(3x2+27x2+2)1/x2[Indeterminate form 1∞] ∴L=elimx→01x2(3x2+27x2+2−1) =elimx→01x2(−4x27x2+2) =1e2

$lim x \to 0 {(\frac{3 x^{2} + 2}{7 x^{2} + 2})}^{1 / x^{2}}$ is equal to: