hi-everybody-for-f-x-x-x-2-ln-1-t-2-t-dt-1-find-the-domain-of-f-and-prove-that-f-is-even-2-prove-that-f-is-differentiable-on-R-find-f-x-3-determine-the-expansion-limited-

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Question Number 139153 by henderson last updated on 23/Apr/21

$$\mathbf{hi},\mathbf{everybody}!$$$$\mathbf{for}f\left(x\right)={\int }_x^{x^2}\frac{ln(1+t^2)}{t}dt$$$$1.\mathbf{find}\mathbf{the}\mathbf{domain}\mathbf{of}f,\mathbf{and}\mathbf{prove}\mathbf{that}f\mathbf{is}\mathbf{even}.$$$$2.\mathbf{prove}\mathbf{that}f\mathbf{is}\mathbf{differentiable}\mathbf{on}\mathbb{R},\mathbf{find}f{}^{{}^{\prime }}\left(x\right).$$$$3.\mathbf{determine}\mathbf{the}\mathbf{expansion}\mathbf{limited}\mathbf{to}\mathbf{order}4\mathbf{of}f$$$$\mathbf{in}0.$$

Commented by greg_ed last updated on 23/Apr/21

$$\mathrm{this}\mathrm{thing}\mathrm{looks}\mathrm{very}\mathrm{interesting}:\mathrm{we}{\mathrm{shouldn}}^{\prime }\mathrm{t}$$$$\mathrm{ignore}\mathrm{it},\mathrm{guyz}!$$

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