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Question Number 86578 by Omer Alattas last updated on 29/Mar/20

Commented by john santu last updated on 29/Mar/20

$$\mathrm{let}\mathrm{F}\left(\mathrm{x}\right)\mathrm{antiderivative}\mathrm{f}\left(\mathrm{x}\right)=\int \underset{3}{\stackrel{\mathrm{x}}{}}\frac{\sin \mathrm{t}\mathrm{dt}}{\mathrm{t}}$$$$\mathrm{such}\mathrm{that}\mathrm{f}\left(\mathrm{x}\right)=\mathrm{F}\left(\mathrm{x}\right)-\mathrm{F}\left(3\right)$$$$\mathrm{now}\underset{x\to 3}{\lim }\frac{\mathrm{x}(\mathrm{F}\left(\mathrm{x}\right)-\mathrm{F}\left(3\right))}{\mathrm{x}-3}=$$$$3\times \underset{x\to 3}{\lim }\frac{\mathrm{F}\left(\mathrm{x}\right)-\mathrm{F}\left(3\right)}{\mathrm{x}-3}\left[{\mathrm{L}}^{\prime }\mathrm{hopital}\mathrm{rule}\right]$$$$3\times {\mathrm{F}}^{\prime }\left(3\right)=3\times \frac{\sin \left(3\right)}{3}=\sin \left(3\right)$$

Commented by Omer Alattas last updated on 29/Mar/20

$$thnks$$

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