Category: Differentiation

Question Number 94245 by mhmd last updated on 17/May/20 $$findthefunctionf\left(x\right)satisfyingthegivenconditions$$$$\left(i\right)f^{{}^{\prime }}\left(x\right)=4x^2-1,f\left(0\right)=3?$$$$\left(ii\right)f^{{}^{″}}\left(x\right)=12,f^{{}^{\prime }}\left(0\right)=2,f\left(0\right)=3?$$$$\left(iii\right)f^{{}^{″}}\left(x\right)=2x,f^{{}^{\prime }}\left(0\right)=-3,f\left(0\right)=2?$$$$ \…

Question Number 159719 by tounghoungko last updated on 20/Nov/21 $$F\left(x\right)=3\cos x+4\sin x,F^{\left(101\right)}\left(\frac{\pi }{2}\right)=?$$ Answered by mathmax by abdo last updated on 20/Nov/21 $$\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)=\mathrm{3cos}\left(\mathrm{x}+\frac{\mathrm{n}\pi}{\mathrm{2}}\right)+\mathrm{4sin}\left(\mathrm{x}+\frac{\mathrm{n}\pi}{\mathrm{2}}\right) \…

Question Number 94125 by i jagooll last updated on 17/May/20 $$\mathrm{Given}\mathrm{a}\mathrm{function}$$$$\mathrm{H}\left(\mathrm{x}\right)=\mid \sin \mathrm{x}+\cos \mathrm{x}\mid +\sqrt{2}\cos \mathrm{x}$$$$\mathrm{with}\mathrm{x}\in [0,2\pi ]$$$$\mathrm{find}\mathrm{H}{\left(\mathrm{x}\right)}_{\max }\mathrm{and}\mathrm{H}{\left(\mathrm{x}\right)}_{\min }$$ Answered by john santu last…

Question Number 159648 by cortano last updated on 19/Nov/21 $$y=\sin {}^2\left(2x\right)$$$$y^{\left(n\right)}=?$$ Answered by FongXD last updated on 19/Nov/21 $$\bullet\:\mathrm{y}=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}−\mathrm{cos4x}\right)=\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos4x} \…

Question Number 159592 by mnjuly1970 last updated on 19/Nov/21 $$$$$$calculate:$$$$$$$$\mathcal{I}:={\int }_0^{\mathrm{\infty }}{\left(\frac{arctan\left(x\right)}{x}\right)}^{3}dx=?$$$$$$ Answered by…