Answer:
t approaches 0 is 2.
Step by step:
To evaluate the limit of the expression (√(a+t) - √(a-t))/t as t approaches 0, we can use the following approach:
1. Start by rationalizing the numerator:
Multiply both the numerator and denominator by the conjugate of the numerator, which is (√(a+t) + √(a-t)).
[(√(a+t) - √(a-t))/(t)] * [((√(a+t) + √(a-t)) / (√(a+t) + √(a-t))]
2. Simplify the numerator:
(√(a+t))^2 - (√(a-t))^2
(a+t) - (a-t)
2t
3. Simplify the denominator:
t
4. Now, simplify the expression:
(2t)/(t)
2
Therefore, the limit of (√(a+t) - √(a-t))/t as t approaches 0 is 2.