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Let f:[1,3[ rarr [0, oo) be continuous a...

Let `f:[1,3[ rarr [0, oo)` be continuous and differentiable function and if `(f(3)-f(1)).(f^(2)(3)+f^(2)(1)+f(3)f(1)=kf^(2)(c)f^(')(c) where c in (1,3)`, then find the value of k.

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