17.3k views
3 votes
What is lim x->1 (x^3-1)/(x-1)?

What is lim x->1 (x^3-1)/(x-1)?-example-1

1 Answer

0 votes

The answer is 3.

Given lim x->1 (x^3 - 1)/(x-1)

First, we need to convert numerator and denominator into simpler terms.

=> (x^3 - 1) / (x - 1)

=> (x^3 - 1^3) / (x - 1)

(x^3 - 1^3) can be written as (x - 1)(x^2 + x + 1^2) if we apply the formula

(a^3 - b^3) = (a-b)(a^2 + ab b^2)

=> (x - 1)(x^2 + x + 1^2) / (x-1)

=> x^2 + x + 1

Now, we re-write the given limit as lim x->1 (x^2 + x + 1). Substitute x = 1 in the expression, we get

1^2 + 1 + 1

= 1 + 1 + 1

= 3

User Tyler Benzing
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories