Limit Values

Calculus Level 3

Suppose f(x)=x4+ax2+bx f(x) = x^4 + ax^2 + bx satisfies the following two conditions:

limx2f(x)f(2)x2=4,limx1f(x)f(1)x21=9.  \lim_{x \to 2} \frac{f(x)-f(2)}{x-2} = 4,\quad \lim_{x \to 1} \frac{f(x)-f(1)}{x^2-1} = 9.\

What is the value of ba? b-a?

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