Respuesta:
1/(2√x) (x>0)
Explicación paso a paso:
Sea h∈(-1,1)-{0} y x>0, entonces
[tex] \frac{ \sqrt{x + h} - \sqrt{x} }{h} = \frac{ \sqrt{x + h} - \sqrt{x} }{h} \cdot \: \frac{ \sqrt{x + h} + \sqrt{x} }{ \sqrt{x + h} + \sqrt{x}} = \frac{1}{ \sqrt{x + h} + \sqrt{x}} [/tex]
Luego si h->0, entonces
[tex] \frac{1}{ \sqrt{x + h} + \sqrt{x}} \rightarrow \: \frac{1}{ \sqrt{x} } [/tex]
" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2024 KUDO.TIPS - All rights reserved.
Verified answer
Respuesta:
1/(2√x) (x>0)
Explicación paso a paso:
Sea h∈(-1,1)-{0} y x>0, entonces
[tex] \frac{ \sqrt{x + h} - \sqrt{x} }{h} = \frac{ \sqrt{x + h} - \sqrt{x} }{h} \cdot \: \frac{ \sqrt{x + h} + \sqrt{x} }{ \sqrt{x + h} + \sqrt{x}} = \frac{1}{ \sqrt{x + h} + \sqrt{x}} [/tex]
Luego si h->0, entonces
[tex] \frac{1}{ \sqrt{x + h} + \sqrt{x}} \rightarrow \: \frac{1}{ \sqrt{x} } [/tex]