Convergence of this priori error in FEM?

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Problem

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My attempt

I think h is the size of the mesh. C is a constant which probably depends on the size of the mesh, I think. I think the error converges linearly and dependent on the size of the mesh. However, I think this is not what is wanted here.

Extension by Daw's comment

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What can you say about the converge of this priori estimate?