Question

suppose f and g are continuous functions such that g ( 2 ) = 5 and lim x → 2 [ 3 f ( x ) f ( x ) g ( x ) ] = 16 . find f ( 2 ) .

Answer 1

To find f(2), use the given information: g(2) = 5 and lim x → 2 [ 3f(x) f(x) g(x) ] = 16. Substitute the values into the equation 3[f(2)]^2 * 5 = 16 and solve for f(2).

Step-by-step explanation:

To find f(2), we need to use the given information. We know that g(2) = 5 and lim x → 2 [ 3f(x) f(x) g(x) ] = 16. We can rewrite the limit expression as 3[f(x)]^2 * g(x). Since the limit evaluates to 16, we can write the equation 3[f(2)]^2 * 5 = 16. Simplifying this equation gives us [f(2)]^2 = 16/15. Taking the square root of both sides gives us f(2) = ±√(16/15).