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lim-a-x-1-b-x-1-c-x-1-a-b-c-1-x-x-0-

Question Number 127358 by Fareed last updated on 29/Dec/20 $$ \\ $$$$\mathrm{lim}\left(\frac{\mathrm{a}^{\mathrm{x}+\mathrm{1}} +\mathrm{b}^{\mathrm{x}+\mathrm{1}} +\mathrm{c}^{\mathrm{x}+\mathrm{1}} }{\mathrm{a}+\mathrm{b}+\mathrm{c}}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} =? \\ $$$$\mathrm{x}\Rightarrow\mathrm{0} \\ $$ Answered by Ar Brandon last…

Question-192884

Question Number 192884 by 073 last updated on 30/May/23 Commented by witcher3 last updated on 03/Jun/23 $$\mathrm{let}\:\mathrm{u}=\mathrm{x}+\mathrm{y},\mathrm{v}=\mathrm{x}−\mathrm{y} \\ $$$$\mathrm{g}\left(\mathrm{u},\mathrm{v}\right)=\left(\mathrm{x},\mathrm{y}\right) \\ $$$$\mathrm{J}_{\mathrm{g}} =\begin{pmatrix}{\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}}\\{\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:−\frac{\mathrm{1}}{\mathrm{2}}}\end{pmatrix} \\ $$$$\begin{pmatrix}{\mathrm{x}}\\{\mathrm{y}}\end{pmatrix}=\frac{\mathrm{1}}{\mathrm{2}}\begin{pmatrix}{\mathrm{u}+\mathrm{v}}\\{\mathrm{u}−\mathrm{v}}\end{pmatrix} \\…

lim-x-6-x-2-x-4-x-

Question Number 61791 by naka3546 last updated on 08/Jun/19 $$\underset{{x}\:\rightarrow\:\infty} {\mathrm{lim}}\:\:\:\frac{\mathrm{6}^{{x}} }{\mathrm{2}^{{x}} \:+\:\mathrm{4}^{{x}} }\:\:\:=\:\:\:\infty\:\:\:\:\:? \\ $$ Commented by mr W last updated on 08/Jun/19 $$\underset{{x}\:\rightarrow\:\infty}…

f-x-function-pair-and-0-decreases-in-the-range-f-x-f-3-solve-the-inequality-

Question Number 127322 by MathSh last updated on 28/Dec/20 $${f}\left({x}\right)\:{function}\:{pair}\:{and}\:\left(−\infty;\mathrm{0}\right] \\ $$$${decreases}\:{in}\:{the}\:{range} \\ $$$${f}\left({x}\right)\geqslant{f}\left(−\mathrm{3}\right)\:{solve}\:{the}\:{inequality} \\ $$ Answered by mindispower last updated on 28/Dec/20 $$\left.\right]\left.−\infty,−\mathrm{3}\right]\cup\left[\mathrm{3},+\infty\left[\right.\right. \\…