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Question Number 214719 by RoseAli last updated on 18/Dec/24

Answered by som(math1967) last updated on 18/Dec/24

$$letx-1=a$$$$x\to 1\Rightarrow (x-1)\to 0\Rightarrow a\to 0$$$$\underset{a\to 0}{lim}\frac{sina}{a}=1$$

Answered by sayedahmad last updated on 18/Dec/24

$$1$$

Answered by MathematicalUser2357 last updated on 18/Dec/24

$$\underset{x\to 1}{\lim }\frac{\sin (x-1)}{x-1}$$$$\mathrm{We}\mathrm{can}\mathrm{simplify}x\to 1\mathrm{to}x-1\to 0.$$$$\mathrm{Let}a=x-1,\mathrm{Use}\mathrm{limit}\mathrm{idenity}$$$$=\underset{a\to 0}{\lim }\frac{\sin a}{a}=1$$

Answered by MrGaster last updated on 19/Dec/24

$$\underset{x\to 1}{\lim }\frac{\sin (x-1)}{x-1}\underbrace{\to \underset{t\to 0}{}\lim }\left(\frac{\sin \left(t\right)}{t}\right)=1.$$

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