# How do you evaluate #sqrt(25-x^2)# as x approaches 5-?

As

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See below.

Here is the reasoning:

More formally,

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As x approaches 5-, the expression sqrt(25-x^2) can be evaluated as follows:

- Substitute the value of x into the expression: sqrt(25-(5-)^2).
- Simplify the expression inside the square root: sqrt(25-(25-10x+x^2)).
- Further simplify the expression: sqrt(25-25+10x-x^2).
- Combine like terms: sqrt(10x-x^2).
- Since x approaches 5-, substitute this value into the expression: sqrt(10(5-)-(5-)^2).
- Simplify the expression: sqrt(50-10-25+10x-x^2).
- Combine like terms: sqrt(25+10x-x^2).

Therefore, as x approaches 5-, sqrt(25-x^2) simplifies to sqrt(25+10x-x^2).

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