Find thllowing limits using agebraic manipulations.
a) lim (4t^2 -t-1)/(t^2 -1) = ?
t--> -1
To find the limit of the given expression, you can directly substitute the value that t is approaching (-1) into the expression and evaluate it. Here's how you can do it step by step:
a) lim (4t^2 -t-1)/(t^2 -1) = ?
t--> -1
Step 1: Substitute the value that t is approaching into the expression:
(4(-1)^2 - (-1) - 1)/((-1)^2 - 1)
Simplifying the numerator:
(4(1) + 1 - 1)/(1 - 1)
(4 + 1 - 1)/(1 - 1)
(4 + 0)/(1 - 1)
4/0
Step 2: Notice that the denominator is equal to 0. This means that the expression is undefined at t = -1, and thus there is no limit for this expression as t approaches -1.
Therefore, the limit does not exist for the expression (4t^2 - t - 1)/(t^2 - 1) as t approaches -1.