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Author: Tinku Tara

Question-227521

Question Number 227521 by mr W last updated on 07/Feb/26 Commented by mr W last updated on 07/Feb/26 As shown in the figure, 100 wooden blocks, each with weight 5 N, are clamped by two forces of magnitude F from the left and right. All contact surfaces have the same roughness. What is the friction force between block No. 27 and block No. 28? Which friction coefficient should the contact surfaces at least have? Terms of Service Privacy Policy Contact:…

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Question Number 227509 by Lara2440 last updated on 06/Feb/26 $$\boldsymbol{\mathrm{PLS}}\:\boldsymbol{\mathrm{HELP}}!!!!! \\ $$$$\mathrm{we}\:\mathrm{want}\:\mathrm{to}\:\mathrm{prove}\:\underset{{h}\rightarrow\mathrm{0}^{\pm} } {\mathrm{lim}}\:\frac{\left({x}+{h}\right)^{{n}} −{x}^{{n}} }{{h}}={n}\centerdot{x}^{{n}−\mathrm{1}} \:\mathrm{by}\:\mathrm{using}\:\mathrm{the}\:\boldsymbol{\epsilon}-\boldsymbol{\delta}\:\mathrm{argument} \\ $$$$\mathrm{def}.\:\forall\boldsymbol{\epsilon}>\mathrm{0}\:,\:\exists\boldsymbol{\delta}>\mathrm{0}\:\mathrm{s}.\mathrm{t}.\:\mid{x}−\alpha\mid<\boldsymbol{\delta}\:\Rightarrow\mid{f}\left({x}\right)−{L}\mid<\boldsymbol{\epsilon} \\ $$$$\mathrm{Now},\:\mathrm{we}\:\mathrm{want}\:\mathrm{to}\:\mathrm{show}\:\mathrm{that}\: \\ $$$$\mathrm{for}\:\mathrm{all}\:\boldsymbol{\epsilon}>\mathrm{0}\:,\:\mathrm{Exist}\:\boldsymbol{\delta}>\mathrm{0}\:\mathrm{s}.\mathrm{t}.\:\mid{x}−\alpha\mid<\boldsymbol{\delta}\:\:\mathrm{Implies}\:\mid\frac{{x}^{{n}} −\alpha^{{n}} }{{x}−\alpha}−{n}\centerdot\alpha^{{n}−\mathrm{1}}…

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Question Number 227487 by Lara2440 last updated on 06/Feb/26 $$\mathrm{prove}\:\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left({x}+{h}\right)^{{n}} −{x}^{{n}} }{{h}}={n}\centerdot{x}^{{n}−\mathrm{1}} \\ $$$$\mathrm{for}\:\mathrm{all}\:\epsilon>\mathrm{0}\:\mathrm{Exist}\:\delta>\mathrm{0}\:\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\mathrm{0}<\mid{x}−\xi\mid<\delta\:\:\mathrm{Implies}\:\mid\frac{{f}\left({x}\right)−{f}\left(\xi\right)}{{x}−\xi}−{f}^{\left(\mathrm{1}\right)} \left(\xi\right)\mid<\epsilon \\ $$$$\mathrm{let}'\mathrm{s}\:{f}\left({x}\right)={x}^{{n}} \: \\ $$$$\forall\epsilon>\mathrm{0}\:,\:\exists\delta>\mathrm{0}\:\mathrm{such}\:\mathrm{that}\:\mathrm{0}<\mid{x}−\xi\mid<\delta\:\rightarrow\:\mid\frac{{x}^{{n}} −\xi^{{n}} }{{x}−\xi}−{n}\xi^{{n}−\mathrm{1}}…

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Question Number 227489 by gregori last updated on 04/Feb/26 $$\mathrm{1}+\mathrm{2}−\mathrm{3}−\mathrm{4}+\mathrm{5}+\mathrm{6}−\mathrm{7}−\mathrm{8}+\mathrm{9}+\mathrm{10}−\mathrm{11}−\mathrm{12}+ \\ $$$$…\:+\mathrm{100}\:=? \\ $$ Commented by Tinku Tara last updated on 04/Feb/26 $$\mathrm{3}−\mathrm{7}+\mathrm{11}−\mathrm{15} \\ $$$$\mathrm{3}+\mathrm{11}+\mathrm{19}+\mathrm{27}+\mathrm{35}+..+\mathrm{195}−…