`x in R` के लिए `lim_(x to oo)((x-3)/(x+2))^(x)` बराबर है

Options

A. e
B. `e^(-1)`
C. `e^(-6)`
D. `e^(5)`

Answer

C

Explanation

`lim_(x-> infty) (( x-3)/( x+3 ))^ x `

`lim_(x-> infty)[(x(1-3/x))/(x(1+3/x))]^x`

अंश और हर से `x` कॉमन लेने पर

`[(1-0)/(1+0)]^oo`

`=1^oo`

` lim_(x-> a)[f(x)]^ g(x) `

` lim_(x-> a) f(x)=1`

`lim_(x-> a) g(x)= infty`

`e^( lim_(x-> a))[f(x)-1]* g(x)`

`f(x) = (x - 3)/(x + 3)`

`e^ (lim_ (x-> infty)` `[ (x-3 )/(x+3) -1].x`

`e^ (lim_(x-> infty)``[ (x-3-x-3) /x+3 ].x`

`e^(lim_(x-> infty) )[-6/(x+3)].x`

`e^(lim_(x-> infty) )[-6/(x(1+3/x)]].x`

`= 3/infty = 0`

`e^(lim_(x-> infty) )[-6/(1+3/x)]`

`e^[(-6/1+0)]`

`e^-6`