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Author: Tinku Tara

K-1-y-3-2-x-1-determinant-x-y-2-1-0-1-2-and-then-plot-

Question Number 215908 by MathematicalUser2357 last updated on 21/Jan/25 $$\mathrm{K}.\mathrm{1} \\ $$$${y}=\frac{\mathrm{3}}{\mathrm{2}}{x}+\mathrm{1} \\ $$$$\begin{array}{|c|c|c|c|c|c|}{{x}}&\hline{{y}}\\{−\mathrm{2}}&\hline{}\\{−\mathrm{1}}&\hline{}\\{\mathrm{0}}&\hline{}\\{\mathrm{1}}&\hline{}\\{\mathrm{2}}&\hline{}\\\hline\end{array}\mathrm{and}\:\mathrm{then}\:\mathrm{plot} \\ $$ Answered by Simurdiera last updated on 21/Jan/25 $$\:\underline{{t}} \underline{\underbrace{…

for-any-natural-numbers-m-n-then-m-n-or-m-lt-n-or-m-gt-n-prove-

Question Number 215939 by mokys last updated on 21/Jan/25 $${for}\:{any}\:{natural}\:{numbers}\:{m},{n}\:{then}\:{m}={n}\:{or}\:{m}<{n}\:{or}\:{m}>{n}\:?\:{prove} \\ $$ Answered by MrGaster last updated on 22/Jan/25 $$\forall{m},{n}\in\mathbb{N} \\ $$$${m}={n}\vee{m}<{n}\vee{m}>{n} \\ $$$$\because\mathbb{N}\subset\mathbb{R}\wedge\mathbb{R}\:\mathrm{is}\:\mathrm{totally}\:\mathrm{ordered} \\…

Find-1-lim-x-0-1-cos2x-x-2-2-n-1-n-n-2-3-n-

Question Number 215893 by hardmath last updated on 20/Jan/25 $$\mathrm{Find}: \\ $$$$\left.\mathrm{1}\right)\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}\:−\:\mathrm{cos2x}}{\mathrm{x}^{\mathrm{2}} }\:=\:? \\ $$$$\left.\mathrm{2}\right)\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}=\infty} {\sum}}\:\frac{\mathrm{n}^{\mathrm{2}} }{\mathrm{3}^{\boldsymbol{\mathrm{n}}} }\:=\:? \\ $$ Answered by mathmax…

Find-lim-h-0-x-h-3-x-3-h-

Question Number 215889 by hardmath last updated on 20/Jan/25 $$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{h}}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{x}\:+\:\mathrm{h}\right)^{\mathrm{3}} \:+\:\mathrm{x}^{\mathrm{3}} }{\mathrm{h}}\:=\:? \\ $$ Commented by mr W last updated on 20/Jan/25 $$\rightarrow\frac{\mathrm{2}{x}^{\mathrm{3}} }{\mathrm{0}}\rightarrow\infty…

lim-x-0-cos-2x-cos-6x-1-cos-3x-cos-5x-

Question Number 215884 by golsendro last updated on 20/Jan/25 $$\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{2x}−\mathrm{cos}\:\mathrm{6x}}{\mathrm{1}−\mathrm{cos}\:\mathrm{3x}\:\mathrm{cos}\:\mathrm{5x}}\:=? \\ $$$$\:\:\:\: \\ $$ Answered by oubiji last updated on 20/Jan/25 $$\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{2x}−\mathrm{cos}\:\mathrm{6x}}{\mathrm{1}−\mathrm{cos}\:\mathrm{3x}\:\mathrm{cos}\:\mathrm{5x}}\: \\…