Question

If `lim_(x->1)(x^5-1)/(x-1)=lim_(x->k)(x^4-k^4)/(x^3-k^3),` then k = ______.

Options

• `4/3`

• `15/4`

• `3/4`

• `4/15`

Answer 1

If `lim_(x->1)(x^5-1)/(x-1)=lim_(x->k)(x^4-k^4)/(x^3-k^3),` then k = `underline(15/4)`.

Explanation:

`lim_(x->1)(x^5-1)/(x-1)=lim_(x->1)(x^5-1^5)/(x-1)` = 5     `...[becauselim_(x->a)(x^m-a^m)/(x^n-a^n)=m/na^(m-n)]`

`lim_(x->k)(x^4-k^4)/(x^3-k^3)=4/3k^(4-3)=4/3k`

`therefore 5 = 4/3k =>k=15/4`