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Limits: please show the steps thanks! im really struggling ​

Limits: please show the steps thanks! im really struggling ​-example-1

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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.

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