Question 453993
f is continuous if:


*[tex \LARGE \lim_{x \to 2-} x^2 - 4x - 2 = \lim_{x \to 2+} ax^2 - bx + 3]


*[tex \LARGE -6 = \lim_{x \to 2+} ax^2 - bx + 3]


*[tex \LARGE -6 = 4a - 2b + 3 \Rightarrow 4a - 2b = -9]



and


*[tex \LARGE \lim_{x \to 3-} ax^2 - bx + 3 = \lim_{x \to 3+} 2x - a + b]


*[tex \LARGE 9a - 3b + 3 = 6 - a + b \Rightarrow 10a - 4b = 3]


Here, we have the system of equations


*[tex \LARGE 4a - 2b = -9]
*[tex \LARGE 10a - 4b = 3]

Solving, we get a = 21/2 and b = 51/2.