Question

Lim x tends 3 (x-3)/(√x-√3)=

Answer 1

${\red{\huge{\underline{\mathbb{Question:-}}}}}$

lim x tends to 3

$\frac{x - 3}{ \sqrt{x} - \sqrt{3} }$

${\green {\huge{\underline{\mathbb{Answer:-}}}}}$

lim X tends to 3

$\frac{x - 3}{ \sqrt{x} - \sqrt{3} }$

________________

rationalise the term

lim x tends to 3

$\frac{x - 3}{ \sqrt{x} - \sqrt{3} } \times \frac{ \sqrt{x} + \sqrt{3} }{ \sqrt{x} + \sqrt{3} }$

lim x tends to 3

$\frac{(x - 3) (\sqrt{x} + \sqrt{3} )}{( x - 3) }$

lim x tends to 3

$\sqrt{x} + \sqrt{3}$

put x = 3

then u get 2√3

which is the required answer

I hope it helps you!

Answer 2

Answer:

{\red{\huge{\underline{\mathbb{Question:-}}}}}

Question:−

lim x tends to 3

\frac{x - 3}{ \sqrt{x} - \sqrt{3} }

x

−

3

x−3

{\green {\huge{\underline{\mathbb{Answer:-}}}}}

Answer:−

lim X tends to 3

\frac{x - 3}{ \sqrt{x} - \sqrt{3} }

x

−

3

x−3

________________

rationalise the term

lim x tends to 3

\frac{x - 3}{ \sqrt{x} - \sqrt{3} } \times \frac{ \sqrt{x} + \sqrt{3} }{ \sqrt{x} + \sqrt{3} }

x

−

3

x−3

×

x

+

3

x

+

3

lim x tends to 3

\frac{(x - 3) (\sqrt{x} + \sqrt{3} )}{( x - 3) }

(x−3)

(x−3)(

x

+

3

)

lim x tends to 3

\sqrt{x} + \sqrt{3}

x

+

3

put x = 3

then u get 2√3

which is the required answer

I hope it helps you!

Explanation:

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