To solve a limit involving the difference of two square rooted terms, you can use the conjugate rule. This means multiplying the numerator and denominator of the fraction by the conjugate of the denominator, which is the same expression but with the opposite sign between the terms.
The conjugate of a square rooted term is the same expression but with the opposite sign between the terms. For example, the conjugate of √x + 2 is √x - 2.
The conjugate rule allows us to get rid of the square root in the denominator, making it easier to evaluate the limit. It also helps to simplify the expression and often leads to a solution.
No, the conjugate rule is not the only method to solve limits involving the difference of two square rooted terms. You can also try simplifying the expression by factoring or using other algebraic techniques.
Sure, let's say we have the limit √x - √4 / x - 4 as x approaches 4. Using the conjugate rule, we multiply the numerator and denominator by the conjugate of the denominator, which is √x + 2. This gives us (√x - √4)(√x + 2) / (x - 4)(√x + 2). We can then simplify this expression to (√x^2 - 2√x - 4) / (x^2 - 16). Now, we can substitute x = 4 into this simplified expression and find that the limit is equal to -1/8.