Evaluate the limit:
Limit as x approaches 6 from the right:
Sq.root of (x - 6).
I know the limit is 0, but how do I show this?
Thanks in advance.
To evaluate the given limit, let's go step by step:
1. Start with the given limit: lim(x->6+) √(x-6).
2. Notice that the expression inside the square root is non-negative for x > 6. Therefore, there is no issue with the square root being imaginary.
3. Next, let's substitute the value that x is approaching into the expression. Since we're approaching from the right side (x->6+), we can use a value like x = 6.1 or x = 6.01 to approximate the limit.
4. Plug in the value x = 6.1 into the expression: √(6.1 - 6) = √0.1 = 0.316.
5. Similarly, substitute x = 6.01 into the expression: √(6.01 - 6) = √0.01 = 0.1.
6. As you can see, as the values of x get closer and closer to 6 from the right side, the function output (the square root expression) also gets arbitrarily close to 0.
7. Therefore, we can conclude that the limit as x approaches 6 from the right is 0.
In summary, you can show that the limit is 0 by substituting values of x that approach 6 from the right into the expression and observing that the function output gets closer and closer to 0.