Question

If Lim x tends to a,then find the value
$\sqrt{a + 2x } - \sqrt{3x} \div \sqrt{3a + x } - 2 \sqrt{x} (here \: a \: not \: equal \: to \: zero)$
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Answer 1

Step-by-step explanation:

this form is 0/0 form

(a+2x)^1/2-(3x)^1/2 divided by (3a+x)^1/2-2*(x)^1/2

diff. with respect to x,

2/2(a+2x)^-1/2-3/2(3x)^-1/2divided by 3/2(3a+x)^-1/2-2/2(x)^-1/2

1/√a+2x-3/2√3x divided by 3/2√3a+x-1/√x

then x=a

1/√a+2a-3/2√3a divided by 3/2√3a+a-1/√a

=1/√3a-3/2√3a divided by 3/2√4a-1/√a

= 2/√3