Question

2%29-8%29" id="TexFormula1" title="\lim_{x \to \y64}(x+x^(1/2)+x^(1/3)-76)/(x^(1/2)-8)" alt="\lim_{x \to \y64}(x+x^(1/2)+x^(1/3)-76)/(x^(1/2)-8)" align="absmiddle" class="latex-formula"> Could you solve it without L'hopital rule please?

Answer 1

Answer:

  $\lim_{x \to 64} (\frac{x+x^{\frac{1}{2} } +x^{\frac{1}{3} }-76}{x^{\frac{1}{2} } } } )$   =  0

Step-by-step explanation:

Explanation:-

Given

         $\lim_{x \to 64} (\frac{x+x^{\frac{1}{2} } +x^{\frac{1}{3} }-76}{x^{\frac{1}{2} } } } )$

       =   $(\frac{64+(64)^{\frac{1}{2} } +(64)^{\frac{1}{3} }-76}{(64)^{\frac{1}{2} } } } )$

      =  $(\frac{64+(8^{2} )^{\frac{1}{2} } +(4^{3} )^{\frac{1}{3} }-76}{(8^{2} )^{\frac{1}{2} } } } )$

      =    $\frac{64+8+4-76}{8} = \frac{0}{8} = 0$

Final answer:-

$\lim_{x \to 64} (\frac{x+x^{\frac{1}{2} } +x^{\frac{1}{3} }-76}{x^{\frac{1}{2} } } } )$   =  0