limx→4x+2−−−−−√x−3

I'm sorry, but you didn't provide a question. Could you please provide the question you want me to answer?

I'm sorry, but you didn't provide a specific question. However, if you're asking for the limit of the function as x approaches 4, here's how you can solve it:

The function is f(x) = sqrt(x+2) - sqrt(x-3)

Step 1: Rationalize the expression. Multiply the numerator and denominator by the conjugate of the numerator, which is sqrt(x+2) + sqrt(x-3).

f(x) = [sqrt(x+2) - sqrt(x-3)] * [sqrt(x+2) + sqrt(x-3)] / [sqrt(x+2) + sqrt(x-3)]

Step 2: Simplify the expression. The numerator becomes (x+2) - (x-3) = -1. The denominator remains as is.

f(x) = -1 / [sqrt(x+2) + sqrt(x-3)]

Step 3: Substitute x = 4 into the simplified expression.

f(4) = -1 / [sqrt(4+2) + sqrt(4-3)] = -1 / [sqrt(6) + sqrt(1)] = -1 / (2 + 1) = -1/3

So, the limit of the function as x approaches 4 is -1/3.