If lim x - ax9-a9-x-a-lim x - 54-x- find all possible values of a-

Given lim_x → ax^9 a^9/x a=lim_x → 5 (4+x).....(i) LHS =lim_x → ax^9 a^9/x a =9(a)^9 1=9a^8 ........(ii) RHS =lim_x → 5 (4+x) =4+5 =9.......(iii) Subsituting ...

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Standard XII

Mathematics

Standard Limits to Remove Indeterminate Form

If lim x → ax...

Question

If ${lim}_{x \to a} \frac{x^{9} - a^{9}}{x - a} = {lim}_{x \to 5} (4 + x)$ , find all possible values of a.

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Solution

Given ${lim}_{x \to a} \frac{x^{9} - a^{9}}{x - a} = {lim}_{x \to 5} (4 + x) . . . . . (i)$

$L H S = {lim}_{x \to a} \frac{x^{9} - a^{9}}{x - a}$

$= 9 (a)^{9 - 1} = 9 a^{8} . . . . . . . . (i i)$

$R H S = {lim}_{x \to 5} (4 + x) = 4 + 5 = 9....... (i i i)$

Subsituting (ii)and (iii)in (i),

$9 a^{8} = 9$

$a^{8} = 1$

$\Rightarrow a^{2} = 1$

$\Rightarrow a = 1, a = - 1$

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If limx→ax9−a9x−a=limx→5(4+x), find all possible values of a.

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