Question

If `lim_(x rightarrow 1) (x^4 - 1)/(x - 1)` = `lim_(x rightarrow k) (x^3 - k^3)/(x^2 - k^2)`, then k is ______. 

Options

• `8/3`

• `3/8`

• `3/2`

• `4/3`

Answer 1

If `lim_(x rightarrow 1) (x^4 - 1)/(x - 1)` = `lim_(x rightarrow k) (x^3 - k^3)/(x^2 - k^2)`, then k is `underlinebb(8/3)`. 

Explanation:

Given, `lim_(x rightarrow 1) (x^4 - 1)/(x - 1)` = `lim_(x rightarrow k) ((x^3 - k^3)/(x^2 - k^2))`

Taking L.H.S. `lim_(x rightarrow 1) (x^4 - 1)/(x - 1)` ...`(0/0 "form")`

`lim_(x rightarrow 1) (4x^3)/1` = 4  ...[Using L Hospital's Rule]

∴ `lim_(x rightarrow k) (x^3 - k^3)/(x^2 - k^2)` = 4

⇒ `lim_(x rightarrow k) (3x^2)/(2x)` = 4 ...[Using L Hospital's Rule]

⇒ `3/2k` = 4

⇒ k = `8/3`