Category: Limits

Question Number 93146 by i jagooll last updated on 11/May/20 $$\underset{x\to 0}{\lim }\frac{\underset{0}{\stackrel{\mathrm{x}}{\int }}(\mathrm{a}+\mathrm{bcos}\mathrm{t}+\mathrm{c}\cos \left(2\mathrm{t}\right))\mathrm{dt}}{{\mathrm{x}}^5}=15$$ Commented by i jagooll last updated on 11/May/20…

Question Number 27601 by abdo imad last updated on 10/Jan/18 $$ffonctionnumericalincreasingon]0,1]and$$$${\int }_0^{1}f\left(t\right)dtconvergesprovethat{lim}_{n->\propto }\frac{1}{n}\sum _{k=1}^{n}f\left(\frac{k}{n}\right)$$$$={\int }_0^{1}f\left(t\right)dt.$$ Terms…

Question Number 93033 by i jagooll last updated on 10/May/20 $$\underset{x\to \pi /6}{\lim }{\left(\tan \left(\frac{3\mathrm{x}}{2}\right)\right)}^{\tan \left(3\mathrm{x}\right)}=?$$ Commented by john santu last updated on 10/May/20 $$\mathrm{let}\:\frac{\mathrm{3x}}{\mathrm{2}}\:=\:\mathrm{t}\:\Rightarrow\mathrm{3x}\:=\:\mathrm{2t}\: \…

Question Number 92966 by i jagooll last updated on 10/May/20 $$\underset{x\to -\mathrm{\infty }}{\lim }\frac{6\mathrm{x}+5}{\sqrt{{9\mathrm{x}}^2+4\mathrm{x}-2}}?$$ Commented by i jagooll last updated on 10/May/20 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\frac{\frac{\mathrm{6x}}{\mid\mathrm{x}\mid}+\frac{\mathrm{5}}{\mid\mathrm{x}\mid}}{\:\sqrt{\mathrm{9}+\frac{\mathrm{4}}{\mathrm{x}}−\frac{\mathrm{2}}{\mathrm{x}^{\mathrm{2}}…

Question Number 27327 by Giannibo last updated on 05/Jan/18 $$\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\frac{{\mathrm{x}}^{2\mathrm{n}}}{1+\mid \mathrm{x}\mid +{\mathrm{x}}^{4\mathrm{n}}}$$ Commented by abdo imad last updated on 05/Jan/18 $$=\:{lim}_{{n}−>\propto} \:\:\:\:\frac{/{x}/^{\mathrm{2}{n}}…