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Question Number 116019 by bemath last updated on 30/Sep/20

$$\underset{x\to 0}{\lim }\frac{\frac{d}{dx}\underset{0}{\stackrel{x}{\int }}\sin \left(t^3\right)dt}{2x^4}?$$

Commented by bemath last updated on 30/Sep/20

$$\underset{x\to 0}{\lim }\frac{\sin \left(x^3\right)}{2x^4}=\underset{x\to 0}{\lim }\frac{\sin \left(x^3\right)}{x^3}.\frac{1}{2x}$$$$=\pm \mathrm{\infty }?(isittrue?)$$

Commented by MJS_new last updated on 30/Sep/20

$$\underset{x\to 0}{\lim }\frac{\frac{d}{dx}\left[\underset{0}{\stackrel{x}{\int }}\sin \left(t^3\right)dt\right]}{2x^4}=\underset{x\to 0}{\lim }\frac{\sin x^3}{2x^4}=$$$$=\underset{x\to 0}{\lim }\frac{3\cos x^3}{8x}{\mathrm{doesn}}^{\prime }\mathrm{t}\mathrm{exist}$$

Commented by bemath last updated on 30/Sep/20

$$thankyousirforyourcorrection$$

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