Question

qsn number 6 and 10.plz

Answer 1

Step-by-step explanation:

6.

We have,

$\lim _{x \rarr \infty} ( \sqrt{x} - \sqrt{x - 3} )$

$\lim _{x \rarr \infty} \frac{( \sqrt{x} - \sqrt{x - 3})( \sqrt{x} + \sqrt{x - 3} ) }{( \sqrt{x} + \sqrt{x - 3} ) }$

$\lim _{x \rarr \infty} \frac{x - x + 3}{ \sqrt{x} + \sqrt{x - 3} }$

$\lim _{x \rarr \infty} \frac{3}{ \sqrt{x} + \sqrt{x - 3} }$

$= \frac{3}{ \infty }$

$= 0$

10.

Since, the points (2,6) , (3,8) and (-1, y) lie in a straight line,

so their slope will be equal

$\frac{8 - 6}{3 - 2} = \frac{y - 6}{ - 1 - 2}$

$\implies \frac{2}{1} = \frac{y - 6}{ - 3}$

$\implies2 \times ( - 3)= y - 6$

$\implies - 6 = y - 6$

$\implies \: y = 0$