Question

How do you find the constants a and b such that the function is continuous on the entire real line for f(x)={x^3, x≤2 and ax^2, x>2

Answer 1

`\lim_(x \to 2) f(x) = f(2)`

In your case, 2^3 = a * 2^2 <=> 8 = a * 4 <=> a = 8 / 4 <=> a = 2.