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Let $a,b,g,h$ be real numbers. How to prove that the functional $F\colon L^2 [a,b]\to \mathbb{R}$, given by $F(u)=\int_a^b (u^2(x)-gu(x)-h)\,dx$ is continuous?

Thank you

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    Thank you Jose27. Is it clear that if $\|u_n\|\to \infty$, then $F(u_n)\to\infty$ as well?2011-09-14
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    @MaxTilt: you should probably post your request for clarification and follow-ups as a comment _to the answer itself_, rather than as a comment to the question. By commenting _on the answer_ the user (in this case Jose27) will get notified of your request/comment. By leaving your comment on the main question the user will not know you have a follow-up question.2011-09-14

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