The correct option is A 2 lim_x→ 1x+1/√(x^2+3) 2 =lim _ x→ 1 (x+1)(√( x^ 2 +3 ) +2) / x^ 2 1 =lim _ x→ 1 (√( x^ 2 +3 ) +2) / x 1 ...

You visited us 8 times! Enjoying our articles? Unlock Full Access!

Properties Derived from Trigonometric Identities

limx→ -1x+1/√...

Question

$lim x \to - 1 \frac{x + 1}{\sqrt{x^{2} + 3} - 2}$ =

- 2

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

\frac{1}{2}

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

2

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

0

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

Open in App

Solution

The correct option is A $- 2$
$lim x \to - 1 \frac{x + 1}{\sqrt{x^{2} + 3} - 2}$
$= {lim}_{x \to - 1} \frac{(x + 1) (\sqrt{x^{2} + 3} + 2)}{x^{2} - 1}$
$= {lim}_{x \to - 1} \frac{(\sqrt{x^{2} + 3} + 2)}{x - 1}$
$= \frac{4}{- 2} = - 2$

Suggest Corrections

Similar questions

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

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

Evaluate the following one sided limits:

$(i) {lim}_{x \to 2^{+}} \frac{x - 3}{x^{2} - 4}$

$(i i) {lim}_{x \to 2^{-}} \frac{x - 3}{x^{2} - 4}$

$(i i i) {lim}_{x \to 0^{+}} \frac{1}{3 x}$

$(i v) {lim}_{x \to 8^{+}} \frac{2 x}{x + 8}$

$(v) {lim}_{x \to 0^{+}} \frac{2}{x^{\frac{1}{5}}}$

$(v i) {lim}_{x \to \frac{π^{-}}{2}} t a n x$

$(v i i) {lim}_{x \to \frac{π}{2^{+}}} s e c x$

$(v i i i) {lim}_{x \to 0^{-}} \frac{x^{2} - 3 x + 2}{x^{3} - 2 x^{2}}$

$(i x) {lim}_{x \to - 2^{+}} \frac{x^{2} - 1}{2 x + 4}$

$(x) {lim}_{x \to 0^{+}} (2 - c o t x)$

$(x i) {lim}_{x \to 0^{-}} 1 + c o s e c x$

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

{lim}_{x \to 2} \frac{x^{3} - 3 x^{2} + 4}{x^{4} - 8 x^{2} + 16}

{lim}_{x \to 1} [\frac{2}{1 - x^{2}} + \frac{1}{x - 1}]

{lim}_{x \to - 3} [\frac{1}{x^{2} + 4 x + 3} + \frac{1}{x^{2} + 8 x + 15}]

Join BYJU'S Learning Program