Answer:
[tex]\lim_{x \to 64} (\frac{x+x^{\frac{1}{2} } +x^{\frac{1}{3} }-76}{x^{\frac{1}{2} } } } )[/tex] = 0
Step-by-step explanation:
Explanation:-
Given
[tex]\lim_{x \to 64} (\frac{x+x^{\frac{1}{2} } +x^{\frac{1}{3} }-76}{x^{\frac{1}{2} } } } )[/tex]
= [tex](\frac{64+(64)^{\frac{1}{2} } +(64)^{\frac{1}{3} }-76}{(64)^{\frac{1}{2} } } } )[/tex]
= [tex](\frac{64+(8^{2} )^{\frac{1}{2} } +(4^{3} )^{\frac{1}{3} }-76}{(8^{2} )^{\frac{1}{2} } } } )[/tex]
= [tex]\frac{64+8+4-76}{8} = \frac{0}{8} = 0[/tex]
Final answer:-
[tex]\lim_{x \to 64} (\frac{x+x^{\frac{1}{2} } +x^{\frac{1}{3} }-76}{x^{\frac{1}{2} } } } )[/tex] = 0
