Question

Derive the below formula :—
${\large{\boxed{ \lim _{x \to a} \frac{ \sf \: \: \: {x}^{n} - {a}^{n} \: \: }{ \sf x - a} = n \sf {a}^{(n - 1)} }}}$

☺ topic — Calculus

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Answer 1

$\huge \blue {\sf{ᴀɴsᴡᴇʀ :- }}$

ғ(x) = xⁿ-ᴀⁿ/x-ᴀ

ғ'(x) = (x-ᴀ) ᴅ/ᴅx(xⁿ-ᴀⁿ) - (xⁿ-ᴀⁿ)ᴅ/ᴅx(x-ᴀ)/(x-ᴀ)²

=> (x-ᴀ) ( ɴxⁿ-¹) - (xⁿ-ᴀⁿ)(1)/(x-ᴀ)²

=> (ɴ-1)xⁿ - ɴᴀxⁿ-1 +ᴀⁿ/(x-ᴀ)²

Answer 2

Explanation:

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