find the limit
u->
sqr(u^4 + 3u+ 6)
To find the limit as u approaches infinity of the given function, you can proceed as follows:
1. Start by simplifying the expression inside the square root:
sqr(u^4 + 3u + 6)
2. Since we are interested in the limit as u approaches infinity, we can focus on the term with the highest power of u, which is u^4.
3. Divide all the terms inside the square root by u^4:
sqr((u^4 + 3u + 6) / u^4)
4. Simplify the expression inside the square root:
sqr(1 + (3/u^3) + (6/u^4))
5. Now, as u approaches infinity, the terms (3/u^3) and (6/u^4) tend to zero. This is because any number divided by a very large number becomes extremely small, approaching zero.
6. Therefore, we can ignore the terms (3/u^3) and (6/u^4) as u approaches infinity. The expression inside the square root simplifies to just 1.
7. Finally, taking the square root of 1 gives us the limit as u approaches infinity:
sqrt(1) = 1
So, the limit as u approaches infinity of sqr(u^4 + 3u + 6) is 1.