Category: Limits

Question Number 166627 by cortano1 last updated on 23/Feb/22 $$\mathrm{If}\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}+{\mathrm{x}}^3+{\mathrm{x}}^5+\dots +{\mathrm{x}}^{\mathrm{n}}\mathrm{and}$$$$\underset{x\to 1}{\lim }\frac{{\mathrm{f}}^2\left(\mathrm{x}\right)-{\mathrm{f}}^2\left(1\right)}{\mathrm{x}-1}=2^{10}\mathrm{then}\mathrm{n}=?$$ Commented by MJS_new last…

Question Number 166612 by mnjuly1970 last updated on 23/Feb/22 $$$$$${\int }_0^{\frac{\pi }{2}}\frac{1}{1+cos\left(x\right)+2sin\left(x\right)}dx=?$$ Commented by cortano1 last updated on 23/Feb/22 $$\:\mathrm{1}+\mathrm{cos}\:\mathrm{x}+\mathrm{2sin}\:\mathrm{x}=\:\mathrm{cos}\:^{\mathrm{2}} \frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}+\mathrm{sin}\:^{\mathrm{2}}…

Question Number 166606 by mathlove last updated on 23/Feb/22 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 166572 by qaz last updated on 22/Feb/22 $$\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\underset{\mathrm{k}=0}{\sum ^{2\mathrm{n}}}{2}^{-\mathrm{k}}\cos \sqrt{\frac{\mathrm{k}}{\mathrm{n}}}=?$$ Answered by alephzero last updated on 23/Feb/22 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{k}=\mathrm{0}}…

Question Number 166522 by mnjuly1970 last updated on 21/Feb/22 Commented by CAIMAN last updated on 21/Feb/22 1 Answered by MJS_new last updated on 21/Feb/22 $$\underset{{x}\rightarrow\mathrm{0}}…