Category: Differentiation

Question Number 191796 by mathlove last updated on 30/Apr/23 Commented by mathlove last updated on 01/May/23 $$pleassolvethis$$ Answered by AST last updated on…

Question Number 126070 by benjo_mathlover last updated on 17/Dec/20 Commented by liberty last updated on 17/Dec/20 $$h\left(x\right)={\int }_1^{x}f\left(t\right)dt\iff h^{\prime }\left(x\right)=f\left(x\right)$$$$h^{\prime }\left(4\right)=f\left(4\right)=2$$$$$$…

Question Number 126010 by bramlexs22 last updated on 16/Dec/20 Answered by liberty last updated on 16/Dec/20 $$TheareaofatringleisA=\frac{1}{2}\left(8\right)\left(6\right)\sin \theta$$$$A=24\sin \theta$$$$\frac{dA}{dt}=\left(24\cos \theta \right)\frac{d\theta }{dt};where\frac{d\theta }{dt}=0.12rad/sec$$$$\Leftrightarrow\:\frac{{dA}}{{dt}}\:=\:\mathrm{24}×\mathrm{0}.\mathrm{12}×\mathrm{cos}\:\frac{\pi}{\mathrm{6}}=\:\mathrm{2}.\mathrm{49}\:{m}^{\mathrm{2}} /{sec}\: \…

Question Number 126003 by mnjuly1970 last updated on 16/Dec/20 $$\dots niceintegral\dots$$$$provethat::$$$$\varphi ={\int }_0^{\frac{\pi }{2}}tan\left(x\right)ln\left(sin\left(x\right)\right)ln\left(cos\left(x\right)\right)dx=\frac{\zeta (3}{8}$$$$\mathcal{G}oodluck$$ Answered by Olaf last updated…

Question Number 125995 by liberty last updated on 16/Dec/20 Commented by benjo_mathlover last updated on 16/Dec/20 $$f\left(x\right)=\{\begin{array}{l}x;0⩽x⩽1\\ -x;-1⩽x⩽0\end{array}$$$$f{}^{\prime }(-1)=\underset{h\to 0}{\lim }\frac{f(-1+h)-f(-1)}{h}$$$$f{}^{\prime }(-1)=\underset{h\to 0}{\lim }\frac{-(-1+h)-\left(1\right)}{h}$$$$\:{f}\:'\left(−\mathrm{1}\right)=\:\underset{{h}\rightarrow\mathrm{0}}…