# limx tends to infinity {x-(x2+x)1/2}

2061 Points
9 years ago
first we will take
x common from the braces
then substitute x = indinity
the would have been their 0

approve if useful
2061 Points
9 years ago
2061 Points
9 years ago
so sorry
we have to rationalise it first
then the term of x square will be cancelled
then divide the complete expression
you will get the answer a 1

approve if useful
2061 Points
9 years ago

then divide the complete expression
you will get the answer a 1

hey it will be

then divide the complete expression  by x and substiture x equals infinity
you will get the answer equal to 1

approve if useful
2061 Points
9 years ago
after rationalising you can too apply l’hospital rule
Prince Sharma
40 Points
9 years ago
SOLUTION:
limx tends to infinity {x-(x2+x)1/2}
first solve the algebra by replacing x by 1/t
{1/t-(1/t2 +1/t)½}
{1/t-(1+t)1/2/t}
{(1-(1+t)1/2)/t}
now rationalise
-t/t(1+(1+t)1/2)
now put the equation in limits
limx tends to infinity -1/(1+(1+1/x)1/2)=   -1/2