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Question Number 31838 by Joel578 last updated on 15/Mar/18

$$\mathrm{Given}$$$$f\left(x\right)=\frac{3}{16}\left({\int }_0^{1}f\left(x\right)dx\right)x^2-\frac{9}{10}\left({\int }_0^{2}f\left(x\right)dx\right)x+2\left({\int }_0^{3}f\left(x\right)dx\right)+4$$$$\mathrm{Solve}$$$$\underset{\mathrm{t}\to 0}{\lim }\frac{2t+\left({\int }_{f\left(2\right)+2}^{f^{-1}\left(t\right)}{\left[f{}^{\prime }\left(x\right)\right]}^{2}dx\right)}{1-\cos t\cosh 2t\cos 3t}$$

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