Final answer:
To find the linear approximation of sqrt(25-x²) near a given point, use the concept of tangent lines.
Step-by-step explanation:
To find the linear approximation of sqrt(25-x²) near a given point, we need to use the concept of tangent lines. Let's consider point (a, f(a)), where a is the x-coordinate of the given point and f(a) is the corresponding y-coordinate. The linear approximation is given by the equation:
y = f(a) + f'(a)(x-a)
where f'(a) is the derivative of the function at x=a. In this case, the derivative of sqrt(25-x²) is -x/(sqrt(25-x²)), so the linear approximation near the given point can be written as:
y = sqrt(25-a²) - (x-a)(a/sqrt(25-a²))