Question Number 1369 by 123456 last updated on 25/Jul/15 $$\mathrm{lets}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{continuous}\:\mathrm{and}\:\mathrm{differentiable} \\ $$$$\mathrm{compute} \\ $$$${g}\left({x}\right)=\underset{\Delta{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{e}^{{f}\left({x}+\Delta{x}\right)} −{e}^{{f}\left({x}\right)} }{{f}\left({x}+\Delta{x}\right)−{f}\left({x}\right)} \\ $$ Answered by prakash jain last updated…
Question Number 1368 by prakash jain last updated on 25/Jul/15 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{ln}\left({ax}+{b}\right)}{\mathrm{ln}\:\left({bx}+{a}\right)}\:=? \\ $$ Commented by 123456 last updated on 25/Jul/15 $${f}\left({x}\right)=\frac{\mathrm{ln}\:\left({ax}+{b}\right)}{\mathrm{ln}\:\left({bx}+{a}\right)} \\ $$$$\frac{\frac{{d}}{{dx}}\left[\mathrm{ln}\:\left({ax}+{b}\right)\right]}{\frac{{d}}{{dx}}\left[\mathrm{ln}\:\left({bx}+{a}\right)\right]}=\frac{\frac{{a}}{{ax}+{b}}}{\frac{{b}}{{bx}+{a}}}=\frac{{a}\left({bx}+{a}\right)}{{b}\left({ax}+{b}\right)}\rightarrow\frac{{ab}}{{ba}}=\mathrm{1} \\…
Question Number 132439 by liberty last updated on 14/Feb/21 $$ \\ $$$$\mathrm{it}\:\mathrm{is}\:\mathrm{a}\:\mathrm{known}\:\mathrm{that}\:\mathrm{a}\:\mathrm{particular} \\ $$$$\mathrm{machine}\:\mathrm{will}\:\mathrm{make}\:\mathrm{product}\:\mathrm{with}\: \\ $$$$\mathrm{a}\:\mathrm{qualified}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{90\%}\:\mathrm{when}\:\mathrm{it}\:\mathrm{is} \\ $$$$\mathrm{running}\:\mathrm{well},\:\:\mathrm{but}\:\mathrm{will}\:\mathrm{do}\:\mathrm{so}\:\mathrm{with}\: \\ $$$$\mathrm{a}\:\mathrm{qualified}\:\:\mathrm{rate}\:\mathrm{of}\:\mathrm{only}\:\mathrm{30\%}\:\mathrm{when}\: \\ $$$$\mathrm{it}\:\mathrm{is}\:\mathrm{not}\:\mathrm{running}\:\mathrm{well}.\:\mathrm{The} \\ $$$$\mathrm{probability}\:\mathrm{that}\:\mathrm{machine}\:\mathrm{is}\: \\…
Question Number 132433 by john_santu last updated on 14/Feb/21 Answered by liberty last updated on 14/Feb/21 $$\mathrm{by}\:\mathrm{using}\:\mathrm{Cosine}\:\mathrm{of}\:\mathrm{law}\: \\ $$$$\:\left(\mathrm{r}−\mathrm{0}.\mathrm{5}\right)^{\mathrm{2}} =\mathrm{0}.\mathrm{5}^{\mathrm{2}} +\left(\sqrt{\mathrm{2}}−\mathrm{r}\right)^{\mathrm{2}} −\mathrm{2}×\mathrm{0}.\mathrm{5}×\left(\sqrt{\mathrm{2}}−\mathrm{r}\right)\mathrm{cos}\:\mathrm{45}° \\ $$$$\cancel{\mathrm{r}^{\mathrm{2}} }−\mathrm{r}+\cancel{\frac{\mathrm{1}}{\mathrm{4}}}=\cancel{\frac{\mathrm{1}}{\mathrm{4}}}+\mathrm{2}−\mathrm{2}\sqrt{\mathrm{2}}\mathrm{r}+\cancel{\mathrm{r}^{\mathrm{2}}…
Question Number 132432 by Chhing last updated on 14/Feb/21 $$ \\ $$$$\:\:\mathrm{Solve}\:\:\mathrm{differential}\:\:\mathrm{equations} \\ $$$$\:\:\:\:\mathrm{1}/\:\left(\mathrm{x}^{\mathrm{3}} −\mathrm{1}\right)\mathrm{y}'+\mathrm{xy}=\mathrm{x} \\ $$$$\:\:\:\:\mathrm{2}/\:\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)\mathrm{y}'−\mathrm{xy}+\frac{\mathrm{2x}}{\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }}=\mathrm{0} \\ $$$$\:\:\:\:\mathrm{3}/\:\mathrm{x}^{\mathrm{2}} \left(\mathrm{lnx}\right)\mathrm{y}''+\mathrm{y}=\mathrm{0}\:,\:\mathrm{know}\:\mathrm{that}\:\mathrm{y}=\mathrm{lnx}\:\mathrm{is}\:\mathrm{the}\:\mathrm{answer} \\ $$$$ \\…
Question Number 132434 by Dwaipayan Shikari last updated on 14/Feb/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{cos}\left({n}\right)}{{n}^{\mathrm{2}} } \\ $$ Answered by mnjuly1970 last updated on 14/Feb/21 $$\:\:{solution}: \\…
Question Number 66895 by Kunal12588 last updated on 20/Aug/19 $${x}+{y}+{z}=−{B} \\ $$$${xy}+{yz}+{zx}={C} \\ $$$${xyz}=−{D} \\ $$$${find}\:{x},{y}\:{and}\:{z}\:{in}\:{terms}\:{of}\:{B},{C}\:{and}\:{D} \\ $$ Answered by mr W last updated on…
Question Number 1358 by tabrez8590@gmail last updated on 25/Jul/15 $${solve} \\ $$$${x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{6} \\ $$ Commented by Rasheed Soomro last updated on 25/Jul/15 $${x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{6}=?…
Question Number 66890 by hmamarques1994@gmail.com last updated on 20/Aug/19 $$\: \\ $$$$\:\:\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}} \:+\:\boldsymbol{\mathrm{x}}^{\mathrm{2}\boldsymbol{\mathrm{x}}} \:=\:\mathrm{20} \\ $$$$\: \\ $$$$\:\:\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}} \:=\:? \\ $$$$\: \\ $$ Answered by…
Question Number 1355 by Rasheed Ahmad last updated on 25/Jul/15 $$\mathrm{8}^{{log}\:\left(\mathrm{12}{x}+\mathrm{1}\right)} =\mathrm{4}^{{log}\:\mathrm{27}} \:\:\:,{solve}\:{for}\:{x}. \\ $$ Answered by Yugi last updated on 25/Jul/15 $${Rewriting}\:{the}\:{above}\:{equation}\:{in}\:{base}\:\mathrm{2}\:{gives} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}^{\mathrm{3}{log}\left(\mathrm{12}{x}+\mathrm{1}\right)}…