Answer to Question #113917 in Calculus for Lizwi

Question #113917
Let f(x)=sinx,x=0 and Δx be a small change in x. Find a first approximation to sin(Δx). Use this to say whether sin(Δx)≈Δx is true or false.
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Expert's answer
2020-05-05T20:04:57-0400

Since limΔx0sinΔxΔx=1\lim\limits_{\Delta x\to 0}\frac{\sin\Delta x}{\Delta x}=1, we obtain that Δx\Delta x is a first approximation of sinΔx\sin\Delta x. Then sinΔxΔx\sin\Delta x\approx\Delta x is true.


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