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

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

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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
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