Question

The value of lim x →0 (√x²+1) -1 / (√x² +9) – 3
(a) 4 (b) 3(c) 1 (d) 2
Please answer fast......with explanation.....​

Answer 1

Answer:

3.  [option(b)]

Step-by-step explanation:

   $\lim_{x \to 0} \frac{\sqrt{x^{2}+1}-1 }{\sqrt{x^{2}+ 9}- 3 }$  

=   $\lim_{x \to 0} \frac{\sqrt{x^{2}+1}-1 }{\sqrt{x^{2}+ 9}- 3 }*(\frac{\sqrt{x^{2}+1}+1 }{\sqrt{x^{2}+1}+1 } )*(\frac{\sqrt{x^{2}+9}+3 }{\sqrt{x^{2}+ 9}+3 } )$

=   $\lim_{x \to 0}( \frac{x^{2}+1-1}{x^{2}+9-9} )*(\frac{\sqrt{x^{2}+9}+3 }{\sqrt{x^{2}+1}+1 } )$

=   $\lim_{ x \to 0} (\frac{\sqrt{x^{2}+9}+3 }{\sqrt{x^{2}+1}+1 } )$

=   $\frac{6}{2}$

=   3.