Evaluate the limit using the appropriate Limit Law(s).
lim
t → 2
of (t^44 − 9)/
2t^2 − 3t + 7
since the denominator is not zero at t=2, just plug in t=2 to get the limit. The function is continuous at t=2.
(2^44-9)/9
To evaluate the limit of (t^44 - 9) / (2t^2 - 3t + 7) as t approaches 2, we can use the appropriate Limit Law(s). The Limit Law that will be helpful in this case is the limit of a ratio rule.
The limit of a ratio rule states that if the limits of two functions f(t) and g(t) exist as t approaches a, and g(t) is not equal to 0 at t=a, then the limit of the ratio f(t) / g(t) as t approaches a is equal to the limit of f(t) as t approaches a divided by the limit of g(t) as t approaches a.
Given the function (t^44 - 9) / (2t^2 - 3t + 7), we can find the limits of the numerator and denominator separately and then divide them to find the final result.
1. Let's start with the limit of the numerator, (t^44 - 9), as t approaches 2.
Simply substitute 2 for t in the numerator:
lim t→2 (t^44 - 9) = (2^44 - 9) = (2^88 - 9)
2. Now, let's find the limit of the denominator, (2t^2 - 3t + 7), as t approaches 2.
Substitute 2 for t in the denominator:
lim t→2 (2t^2 - 3t + 7) = (2*2^2 - 3*2 + 7) = (2*4 - 6 + 7) = (8 - 6 + 7) = 9
3. Finally, divide the limits of the numerator and denominator:
lim t→2 (t^44 - 9) / (2t^2 - 3t + 7) = (2^88 - 9) / 9
Therefore, the value of the limit as t approaches 2 is (2^88 - 9) / 9.