Question

निम्नलिखित सीमा का मान प्राप्त कीजिए:

`lim_(x → 0)((x + 1)^5 - 1)/x`

Answer 1

`lim_(x → 0)((x + 1)^5 - 1)/x`

= `lim_(x → 0)((1 + 5x + 10x^2 + 10x^3 + 5x^4 + x^5) - 1)/x`

= `lim_(x → 0) (x(5 + 10x + 10x^2 + 5x^3 + x^4))/x`

= `lim_(x → 0)(5 + 10x + 10x^2 + 5x^3 + x^4)`

= 5

वैकल्पिक विधि: हम जानते हैं:

`lim_(x → a)(x^n - 1)/(x - 1) = na^(n - 1)`

`lim_(x → 0) ((x + 1)^5 - 1)/x`

= `lim_(x → 0) ((x + 1)^5 - 1)/((x + 1) - 1)`

= `lim_(x → 0) 5(x + 1)^4`

= 5