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LIMITS AND DERIVATIVES — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLIMITS AND DERIVATIVES1 Mark
Question
Find the derivative of sin x at x = 0.
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Answer

Let f(x) = sin x. Therefore,
$f^{\prime}(0)=\lim _{h \rightarrow 0} \frac{f(0+h)-f(0)}{h}$
$=\lim _{h \rightarrow 0} \frac{\sin (0+h)-\sin (0)}{h}=\lim _{h \rightarrow 0} \frac{\sin h}{h}=1$

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