Question

Limited X tends to 4 x 3 - 64 upon x 2 - 16​

Answer 1

Question :-

$\displaystyle \red{\lim_{x \to 4}} \green{ \frac{ {x}^{3} - 64}{ {x}^{2} - 16} }$

Answer :-

$\to \boxed{\displaystyle \orange{\lim_{x \to 4}} \pink{ \frac{ {x}^{3} - 64}{ {x}^{2} - 16} } = 6}$

Formula used :-

→ a² - b² = (a - b)(a+b)

→ a³ - b³ = (a - b) (a² +b² +ab)

Explanation :-

$\to \: \displaystyle \purple{\lim_{x \to 4}} \orange{ \frac{ {x}^{3} - 64}{ {x}^{2} - 16} } \\ \: \\ \to \: \displaystyle \red{\lim_{x \to 4}} \green{ \frac{ {x}^{3} - {4}^{3} }{ {x}^{2} - {4}^{2} } } \\ \: \\ \to \: \displaystyle \orange{\lim_{x \to 4}} \green{ \frac{(x - 4)( {x}^{2} + 16 + 4x)}{ \blue{(x - 4)(x + 4)}} } \\ \\ \to \: \displaystyle \blue{\lim_{x \to 4}} \green{ \frac{( {x}^{2} + 16 + 4x)}{ \purple{(x + 4)}} } \\ \sf taking \: limit \\ \\ \to \: \frac{ {4}^{2} + 16 + 16}{4 + 4} \\ \\ \to \: \frac{48}{8} \\ \\ \to \: 6$

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