Question

If Lim x tends to a

x9+a9/x+a = 9


anyone please answer . pleaassss​

Answer 1

Answer:

see the above attachment

Answer 2

Given,

$\[\mathop {\lim }\limits_{x \to a} \left( {\frac{{{x^9} + {a^9}}}{{x + a}}} \right) = 9\]$

Solution,

$\[ \Rightarrow \mathop {\lim }\limits_{x \to a} \left( {\frac{{{x^9} - {{\left( { - a} \right)}^9}}}{{x - \left( { - a} \right)}}} \right) = 9\]$

Differentiate with respect to x,

$\[\begin{array}{l} \Rightarrow 9 \times {x^{9 - 1}} = 9\\ \Rightarrow 9 \times {\left( { - a} \right)^8} = 9\\ \Rightarrow {a^8} = 1\\ \Rightarrow a = \pm 1\end{array}\]$

Hence the value of a is $\[ \pm 1\]$