Limx- a-x-b-a-b-x2-a2- a-b is

The correct option is D 1/4a√(a b) Given, #160; lim_x→ a^ √(x b) √(a b)/x^2 a^2 Substituting gives us indeterminate form.So applying L'Hospitals rul ...

You visited us 3 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Mathematics

Cube-Root of Fractional Numbers

limx→ a-√x-b-...

Question

$lim x \to a^{-} \frac{\sqrt{x - b} - \sqrt{a - b}}{x^{2} - a^{2}}$ , $(a > b)$ is

\frac{1}{4 a}

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

\frac{1}{a \sqrt{a - b}}

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

\frac{1}{2 a \sqrt{a - b}}

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

\frac{1}{4 a \sqrt{a - b}}

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

Open in App

Solution

The correct option is D $\frac{1}{4 a \sqrt{a - b}}$
Given, $lim x \to a^{-} \frac{\sqrt{x - b} - \sqrt{a - b}}{x^{2} - a^{2}}$
Substituting gives us indeterminate form.
So applying L'Hospitals rule,
$= {lim}_{x \to a^{-}} \frac{\frac{1}{2 \sqrt{(x - b)}}}{2 x}$
$= \frac{1}{4 a \sqrt{(a - b)}}$
Hence, option 'D' is correct.

Suggest Corrections

Similar questions

Q. Find the value of

- 1 [a - 3 {b - 4 (a - ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ b - 8) + 4 a} + 10]

if a = 1, b = 0.

Q. The rate of a reaction is expressed in different ways as follows:

\frac{1}{2} (\frac{d [C]}{d t}) = - \frac{1}{3} (\frac{d [D]}{d t}) = \frac{1}{4} (\frac{d [A]}{d t}) = - (\frac{d [B]}{d t})

The reaction is

Q. Show that:
(1)

\sqrt{a^{2} + b} = a + \frac{b}{2 a +} \frac{b}{2 a +} \dots

(2)

\sqrt{a^{2} - b} = a - \frac{b}{2 a -} \frac{b}{2 a -} \dots

Q. If a = 1 and b = 0, find the value of

- 1 [a - 3 {b - 4 (a - ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ b - 8) + 4 a} + 10]

Q. Let

f (x) = \{\begin{matrix} \frac{x - 4}{|x - 4|} + a, & x < 4 \\ a + b, & x = 4 \\ \frac{x - 4}{|x - 4|} + b, & x > 4 \end{matrix} .

Then, f (x) is continuous at x = 4 when
(a) a = 0, b = 0
(b) a = 1, b = 1
(c) a = −1, b = 1
(d) a = 1, b = −1.

Join BYJU'S Learning Program

limx→a−√x−b−√a−bx2−a2, (a>b) is

The correct option is D 14a√a−bGiven, limx→a−√x−b−√a−bx2−a2Substituting gives us indeterminate form.So applying L'Hospitals rule,=limx→a−12√(x−b)2x=14a√(a−b)Hence, option 'D' is correct.

$lim x \to a^{-} \frac{\sqrt{x - b} - \sqrt{a - b}}{x^{2} - a^{2}}$ , $(a > b)$ is