Does the limit lim 2011t/3-(squareroot)t+9 exist ?
t-0
limit approaches 6 x+6/x^2-36
To determine the existence of the limit lim_{t->0} (2011t/3 - sqrt(t) + 9), we can evaluate the limit algebraically using the properties of limits. Here's how you can do it:
1. Simplify the expression inside the limit:
2011t/3 - sqrt(t) + 9
2. Evaluate the limit as t approaches 0 by substituting 0 into the expression:
lim_{t->0} (2011(0)/3 - sqrt(0) + 9)
= 0/3 - 0 + 9
3. Simplify the expression:
= 0 - 0 + 9
= 9
Therefore, the limit of the given expression as t approaches 0 exists and its value is 9.