If lim x - a x 5- a 5- x - a -405- find all possible values of a-

Given lim_x → ax^5 a^5/x a=405 ....(i) LHS =lim_x → ax^5 a^5/x a =5(a)^5 1 =5a^4 It is given that 5a^4 =405 ⇒ 5a^4 =405 a^4 =405/5=81 a^4 =(3)^4, a^2 =9 a= ± ...

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Standard XII

Mathematics

Standard Limits to Remove Indeterminate Form

If lim x → a ...

Question

If ${lim}_{x \to a} \frac{x^{5} - a^{5}}{x - a} = 405$ , find all possible values of a.

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Solution

Given ${lim}_{x \to a} \frac{x^{5} - a^{5}}{x - a} = 405 . . . . (i)$

$L H S = {lim}_{x \to a} \frac{x^{5} - a^{5}}{x - a}$

$= 5 (a)^{5 - 1}$

$= 5 a^{4}$ It is given that $5 a^{4} = 405$

$\Rightarrow 5 a^{4} = 405$

$a^{4} = \frac{405}{5} = 81$

$a^{4} = (3)^{4}, a^{2} = 9$

$a = \pm 3$

$\Rightarrow a = 3$ and a=-3

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If limx→ax5−a5x−a=405, find all possible values of a.

Given limx→ax5−a5x−a=405....(i) LHS=limx→ax5−a5x−a =5(a)5−1 =5a4 It is given that 5a4=405 ⇒5a4=405 a4=4055=81 a4=(3)4,a2=9 a=±3 ⇒a=3 and a=-3

If ${lim}_{x \to a} \frac{x^{5} - a^{5}}{x - a} = 405$ , find all possible values of a.