How do you find $lim t/sqrt(4t^2+1)$ as $t->oo$ ?

Question

1939 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-20T17:15:21

$lim_(trarroo)t/sqrt(4t^2+1)=1/2=0.5$

show below

$lim_(trarroo)t/sqrt(4t^2+1)=lim_(trarroo)[(t)/sqrt[t^2(4+1/(t^2))]]$

$lim_(trarroo)[(t)/(tsqrt[(4+1/(t^2)))]]==lim_(trarroo)1/sqrt(4+1/(t^2))$

$1/sqrt(4+1/(oo))=1/sqrt4=1/2=0.5$

Note that

$color(red)[c/oo]=0$ where c any constant

How do you find lim t/sqrt(4t^2+1)lim t/sqrt(4t^2+1) as t->oot->oo?