Question #0be2a

Question

1572 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-31T19:21:00

$0.$

The Reqd. Lim $=lim_(x to oo)[(2x+2)/(3x-1)]^(3x)$

$=lim {((2x)(1+1/x))/((3x)(1-1/(3x)))]^(3x)$

$=[lim {(2/3)^3}^x][lim {(1+1/x)^x}^3]/[lim {(1+(1/(-3x)))^(-3x)}^(-1)$

$=[lim(8/27)^x][lim {(1+1/x)^x}^3]/[lim {(1+(1/(-3x)))^(-3x)}^(-1)$

Now, recall the following Standard Limits :

$(1) : lim_(y to oo) r^y=0, if |r|<1.$

$(2) : lim_(y to oo) (1+1/y)^y=e.$

$:." The Reqd. Lim="0*[e^3]/[e^(-1)]=0*e^4=0.$

Enjoy Maths.!