Mathematics, 02.09.2020 03:01 SKYBLUE1015
Evaluate the limit with either L'Hôpital's rule or previously learned methods. lim Sin(x)- Tan(x)/ x^3x → 0
Answers: 1
, to evaluate the following steps must be carried out.
![= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ sin(x)-tan(x)]}{\frac{d}{dx} (x^3)}\\= \lim_{ x\to \ 0} \dfrac{cos(x)-sec^2(x)}{3x^2}\\](/tpl/images/0737/7606/61c69.png)
![= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ cos(x)-sec^2(x)]}{\frac{d}{dx} (3x^2)}\\= \lim_{ x\to \ 0} \dfrac{-sin(x)-2sec^2(x)tan(x)}{6x}\\](/tpl/images/0737/7606/34ade.png)
![= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ -sin(x)-2sec^2(x)tan(x)]}{\frac{d}{dx} (6x)}\\= \lim_{ x\to \ 0} \dfrac{[ -cos(x)-2(sec^2(x)sec^2(x)+2sec^2(x)tan(x)tan(x)]}{6}\\\\= \lim_{ x\to \ 0} \dfrac{[ -cos(x)-2(sec^4(x)+2sec^2(x)tan^2(x)]}{6}\\](/tpl/images/0737/7606/ffd12.png)
![= \dfrac{[ -cos(0)-2(sec^4(0)+2sec^2(0)tan^2(0)]}{6}\\\\= \dfrac{-1-2(0)}{6} \\= \dfrac{-1}{6}](/tpl/images/0737/7606/937cf.png)
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Evaluate the limit with either L'Hôpital's rule or previously learned methods. lim Sin(x)- Tan(x)/ x...
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