Question Number 73715 by Learner-123 last updated on 15/Nov/19 $${Evaluate}\:{the}\:{integral}\:: \\ $$$$\underset{\:\mathbb{R}} {\int}\int\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{14}{xy}+\mathrm{8}{y}^{\mathrm{2}} \right){dxdy}\:{for}\:{the}\:{region} \\ $$$$\mathbb{R}\:\mathrm{in}\:{the}\:\mathrm{1}{st}\:{quadrant}\:{bounded}\:{by}\:{the} \\ $$$${lines}\:{y}=\frac{−\mathrm{3}}{\mathrm{2}}{x}+\mathrm{1},{y}=\frac{−\mathrm{3}}{\mathrm{2}}{x}+\mathrm{3},{y}=−\frac{\mathrm{1}}{\mathrm{4}}{x} \\ $$$${and}\:{y}=−\frac{\mathrm{1}}{\mathrm{4}}{x}+\mathrm{1}\:. \\ $$ Commented by…
Question Number 73712 by FCB last updated on 15/Nov/19 Answered by MJS last updated on 15/Nov/19 $$\underset{{x}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\frac{\mathrm{1}}{{x}}\:=−\infty \\ $$$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\frac{\mathrm{1}}{{x}}=+\infty \\ $$$$\Rightarrow\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 8176 by lepan last updated on 02/Oct/16 $${Prove}\:{that}\:{cos}\mathrm{2}\theta=\frac{\mathrm{1}−{tan}^{\mathrm{2}} \theta}{\mathrm{1}+{tan}^{\mathrm{2}} \theta}.{Hence}\:{deduce}\:{that}\: \\ $$$${tan}\mathrm{22}\frac{\mathrm{1}}{\mathrm{2}}=\sqrt{\mathrm{2}}−\mathrm{1}. \\ $$$$ \\ $$$$ \\ $$ Answered by prakash jain last…
Question Number 73710 by Faradtimmy last updated on 15/Nov/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 8175 by prakash jain last updated on 02/Oct/16 $$\mathrm{Prove} \\ $$$$\frac{\mathrm{4}^{{n}} }{{n}}<\:^{\mathrm{2}{n}} {C}_{{n}} \:\mathrm{for}\:\mathrm{all}\:{n}\geqslant\mathrm{4}\:\mathrm{and}\:{n}\in\mathbb{Z}^{+} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 8174 by prakash jain last updated on 02/Oct/16 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{infinite}\:\mathrm{prime} \\ $$$$\mathrm{numbers}\:\mathrm{of}\:\mathrm{the}\:\mathrm{form}\:\mathrm{10}^{{n}} +\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73708 by Faradtimmy last updated on 15/Nov/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73709 by Faradtimmy last updated on 15/Nov/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73707 by Faradtimmy last updated on 15/Nov/19 Commented by Faradtimmy last updated on 16/Nov/19 $${pls}\:{help}\:{me}\:{to}\:{solve}\:{it} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 8168 by aungnaingsoe last updated on 02/Oct/16 $${Find}\:{the}\:{coefficient}\:{of}\:{in}\:{the}\:{expansion}\:{of} \\ $$$$\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{3}} \right)…\left(\mathrm{1}+{x}^{{n}} \right). \\ $$ Commented by Rasheed Soomro last updated on 02/Oct/16…