Can someone help on a calculus problem?

Question

Evaluate the limit thats exists:

lim

X-->1

X^5 - 1 (numerator)

----------------

X^4 - 1 (denominator)

i keep getting 0/0 but the answer for the problem says its 5/4

can someone please help.

Answer 1

  0

Answer 2

x^5 - 1 = (x - 1)(x^4 + x^3 + x^2 + x + 1)

x^4 = (x - 1)(x^3 + x^2 + x + 1)

lim (x^5 - 1) / (x^4 - 1) =

x->1

lim [(x - 1)(x^4 + x^3 + x^2 + x + 1)] / [(x - 1)(x^3 + x^2 + x + 1)] =

x->1

= lim (x^4 + x^3 + x^2 + x + 1) / (x^3 + x^2 + x + 1) =

x->1

= (1^4 + 1^3 + 1^2 + 1 + 1) / (1^3 + 1^2 + 1 + 1) = 5 / 4

Answer 3

factor num and denom:

num becomes:

(x-1)(x^4+x^3+x^2+x+1)

denom becomes:

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

(x^2+1)(x+1)(x-1)

divide these and get:

[x^4+x^3+x^2+x+1]/[(x^2+1)(x+1)]

now when you substitute x->1 you get:

[1+1+1+1+1]/[2x2]=5/4