Calc. question?

How does this equal 4?

lim

X->1

x^4-1

——–

x-1

Top 1 Answers

A few days ago

Anonymous

Favorite Answer

x^4 – 1 can be factorised as the difference of two squares:

(x^2 – 1)(x^2 + 1).

The first factor can again be split the same way, into:

(x – 1)(x + 1).

Thus the factors of x^4 – 1 are:

(x – 1)(x + 1)(x^2 + 1).

On division by x – 1, the limit at x = 1 is the value of:

(x + 1)(x^2 + 1) when x = 1.

That is:

(1 + 1)(1 + 1)

= 2 * 2

= 4.

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