MCQ
$\mathop {\lim }\limits_{x \to a} \frac{{\sqrt {3x - a} - \sqrt {x + a} }}{{x - a}} = $
- A$\sqrt 2 a$
- ✓$1/\sqrt {2a} $
- C$2a$
- D$1/2a$
✓
Answer
Correct option: B.
$1/\sqrt {2a} $
b
(b) $\mathop {\lim }\limits_{x \to a} \,\frac{{\sqrt {3x - a} - \sqrt {x + a} }}{{x - a}}$
(b) $\mathop {\lim }\limits_{x \to a} \,\frac{{\sqrt {3x - a} - \sqrt {x + a} }}{{x - a}}$
$ = \mathop {\lim }\limits_{x \to a} \,\frac{{\sqrt {3x - a} - \sqrt {x + a} }}{{(x - a)}} \times \frac{{\sqrt {3x - a} + \sqrt {x + a} }}{{\sqrt {3x - a} + \sqrt {x + a} }}$
$ = \frac{2}{{2\sqrt {2a} }} = \frac{1}{{\sqrt {2a} }}$
Aliter : Apply $L$- Hospital’s rule
$\mathop {\lim }\limits_{x \to a} \,\frac{{\sqrt {3x - a} - \sqrt {x + a} }}{{x - a}} = \mathop {\lim }\limits_{x \to a} \,\frac{3}{{2\,\sqrt {3x - a} }} - \frac{1}{{2\,\sqrt {x + a} }}$
$ = \frac{3}{{2\sqrt {2a} }} - \frac{1}{{2\sqrt {2a} }} = \frac{1}{{\sqrt {2a} }}.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If R is a relation from a finite set A having m elements of a finite set B having n elements, then the number of relations from A to B is:
- 2mn
- 2mn - 1
- 2mn
- mn
The mean of the following data is :
45, 35, 20, 30, 15, 25, 40:
45, 35, 20, 30, 15, 25, 40:
In a throw of a dice the probability of getting one in even number of throw is
The inequality to represent the coloured region in figure is....
The average can be found only in __________ variables:
The straight line $ y + x = 1 $ touches the parabola :
→The points $1 + 3i,\,5 + i$ and $3 + 2i$ in the complex plane are
→Two sides of a parallelogram are along the lines, $x + y = 3$ and $x -y + 3 = 0$. If its diagonals intersect at $(2, 4)$, then one of its vertex is
→If $\alpha $ and $\beta $ be the roots of the equation $2{x^2} + 2(a + b)x + {a^2} + {b^2} = 0$, then the equation whose roots are ${(\alpha + \beta )^2}$ and ${(\alpha - \beta )^2}$ is
→The equation of the parabola whose axis is vertical and passes through the points $(0, 0), (3, 0)$ and $(-1, 4)$ is
→