Mathematics - Limits Question with Solution | TestHub

If $\mathrm{f}(\mathrm{x})={\lim }_{\mathrm{p}\to \infty }\frac{{\mathrm{x}}^{\mathrm{p}}\mathrm{g}(\mathrm{x})+\mathrm{h}(\mathrm{x})+7}{7{\mathrm{x}}^{\mathrm{p}}+3\mathrm{x}+1};\mathrm{x}\ne 1$ and $\mathrm{f}(1)=7,\mathrm{f}(\mathrm{x}),\mathrm{g}(\mathrm{x})$ and $\mathrm{h}(\mathrm{x})$ are all continuous function at $\mathrm{x}=1$. Then which of the following statement(s) is/are correct