Given,

\(\lim\limits_{\text x \to a}\cfrac{\text x^3-a^3}{\text x-a}=\lim\limits_{\text a\to1}\cfrac{\text x^4-1}{\text x-1} \)

Note: To solve the problems of limit similar to one in our question we use the formula mentioned below which can be derived using binomial theorem.

Formula to be used:\(\lim\limits_{\text x \to a}\cfrac{(\text x)^n-(a)^n}{\text x-a} \)= nan -1

Using the formula we have –

3a3–1 = 4(1)4–1

⇒ 3a2 = 4

⇒ a2 = 4/3

∴ a = ± (2/√3)