Calculate the following limits \lim_{x\rightarrow a}\frac{x^{3}-a^{3}}{x^{4}-a^{4}}

pedzenekO

pedzenekO

Answered question

2021-06-08

Calculate the following limits
limxax3a3x4a4

Answer & Explanation

dieseisB

dieseisB

Skilled2021-06-09Added 85 answers

Step 1
Given
limxax3a3x4a4
We have to evaluate the limit.
Step 2
We have
limxax3a3x4a4
limxa(xa)(x2+xa+a2)(x2a2)(x2+a2) (Done factorization)
limxa(xa)(x2+xa+a2)(x+a)(xa)(x2+a2) (Again done factorization)
limxa(x2+xa+a2)(x+a)(x2+a2) (Cancelling out common factor)
limxa(a2+a×a+a2)(a+a)(a2+a2) (Substituting the limit)
limxa(3a2)(2a)(2a2)
32×(2a)
34a
So,
limxax3a3x4a4=34a

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