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Author: Tinku Tara

sinx-sin-x-2-x-2-ax-cos-6x-dx-

Question Number 4683 by thachan last updated on 21/Feb/16 $$\int_{\boldsymbol{{sinx}}} ^{\mathrm{sin}\:\boldsymbol{{x}}+\mathrm{2}} \left(\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{ax}}+\mathrm{cos}\:\left(\mathrm{6}\boldsymbol{{x}}\right)\right)\boldsymbol{{dx}} \\ $$ Commented by prakash jain last updated on 21/Feb/16 $$\mathrm{The}\:\mathrm{bounds}\:\mathrm{are}\:\mathrm{dependent}\:\mathrm{on}\:{x}? \\…

4-cos-4-x-2-3ax-5tan-x-dx-

Question Number 4681 by thachan last updated on 21/Feb/16 $$\int_{\mathrm{4}} ^{\mathrm{cos}\:\underset{\mathrm{4}} {\prod}} \left({x}^{\mathrm{2}} +\mathrm{3}{ax}βˆ’\mathrm{5tan}\:\left({x}\right)\right){dx} \\ $$ Commented by prakash jain last updated on 21/Feb/16 $${is}\:{the}\:{upper}\:{limit}\:\mathrm{cos}\:\frac{\pi}{\mathrm{4}}?…

Let-a-b-c-d-R-a-b-c-d-0-Prove-that-cyc-1-a-2-a-1-4-

Question Number 4679 by 314159 last updated on 22/Feb/16 $${Let}\:{a},{b},{c},{d}\:\in{R}\:,{a}+{b}+{c}+{d}=\mathrm{0}.{Prove}\:{that} \\ $$$$\underset{{cyc}} {\sum}\left(\frac{\mathrm{1}}{\:\sqrt{{a}^{\mathrm{2}} +{a}+\mathrm{1}}}\right)\leqslant\mathrm{4}. \\ $$ Commented by prakash jain last updated on 21/Feb/16 $$\mathrm{It}\:\mathrm{is}\:\mathrm{not}\:\mathrm{much}\:\mathrm{less}\:\mathrm{than}\:\mathrm{4}.…

x-2-5x-2-0-

Question Number 4674 by thachan last updated on 20/Feb/16 $${x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{2}=\mathrm{0} \\ $$ Answered by FilupSmith last updated on 20/Feb/16 $${x}=\frac{βˆ’{b}\pm\sqrt{{b}^{\mathrm{2}} βˆ’\mathrm{4}{ac}}}{\mathrm{2}{a}} \\ $$$${x}=\frac{βˆ’\mathrm{5}\pm\sqrt{\mathrm{25}βˆ’\mathrm{4}\left(\mathrm{1}\right)\left(\mathrm{2}\right)}}{\mathrm{2}\left(\mathrm{1}\right)} \\…

Define-a-function-f-R-R-such-that-f-f-x-x-2-x-1-for-all-real-x-Evaluate-f-0-

Question Number 4671 by 314159 last updated on 20/Feb/16 $${Define}\:{a}\:{function}\:{f}:{R}\rightarrow{R}\:{such}\:{that}\:{f}\left({f}\left({x}\right)\right)={x}^{\mathrm{2}} βˆ’{x}+\mathrm{1} \\ $$$${for}\:{all}\:{real}\:{x}.{Evaluate}\:{f}\left(\mathrm{0}\right). \\ $$$$ \\ $$ Answered by 123456 last updated on 20/Feb/16 $${f}\left({f}\left({x}\right)\right)={x}^{\mathrm{2}}…