Freeflows
Non Intersecting Graphs Area
Consider the two functions $ f(x) = x^2 + 2bx + 1 $ and $ g(x) = 2a(x + b), $ where the variables $ x $ and the constants $ a $ and $ b $ are real numbers. Each such pair of constants $ a $ and $ b $ may be considered as a point $ (a,b) $ in an $ ab $-plane. Let $ S $ be the set of points $ (a,b) $ for which the graphs of $ y = f(x) $ and $ y = g(x) $ do not intersect (in the $ xy $-plane). Find the area of $ S $.
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- 3
- +
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- -
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- 9
- $\frac{a}{b}$
- .
- 0
- =
- %
- $a^n$
- $a^{\circ}$
- $a_n$
- $\sqrt{}$
- $\sqrt[n]{}$
- $\pi$
- $\ln{}$
- $\log$
- $\theta$
- $\sin{}$
- $\cos{}$
- $\tan{}$
- $($
- $)$
- $[$
- $]$
- $\cap$
- $\cup$
- $,$
- $\infty$