Find the limit.
lim (5u^4+7)/(u^2-2)(2u^2-1)
u-->infinity
Use the same logic that I applied to your other question. Neglect the constant terms.
You should get 5/2 as the limit.
thank you
To find the limit of the given expression as u approaches infinity, we need to evaluate the expression when u becomes a very large number.
First, let's simplify the expression:
(5u^4 + 7) / ((u^2 - 2)(2u^2 - 1))
Next, consider the highest powers of u in the numerator and denominator. In this case, u^4 is the highest power. So we can divide the entire expression by u^4 to simplify it further:
(5 + 7/u^4) / ((u^2 - 2)(2u^2 - 1) / u^4)
Now, let's focus on the denominator expression ((u^2 - 2)(2u^2 - 1) / u^4) as u approaches infinity:
As u becomes very large, the terms involving u^2 dominate the expression. Thus, we can disregard all other terms. Simplifying further, we have:
((u^2 - 2)(2u^2 - 1) / u^4) ≈ (u^2 * 2u^2) / (u^4) = (2u^4) / (u^4) = 2
Now, the entire expression becomes:
(5 + 7/u^4) / 2
As u approaches infinity, 7/u^4 approaches zero because the denominator - u^4 - becomes very large. Therefore, we can ignore it.
So, the final limit is:
(5 + 0) / 2 = 5/2
Hence, the limit of the expression as u approaches infinity is 5/2.