Question

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

Answer 1

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

Explanation:

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