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Author: Tinku Tara

A-plane-has-equation-x-z-4-3-The-line-l-has-vector-equation-r-cos-3-i-2-sin-j-cos-3-k-where-is-a-scalar-parameter-If-l-meets-the-plane-at-P-show-that-as-varies-P-describes

Question Number 1851 by 112358 last updated on 14/Oct/15 $${A}\:{plane}\:{has}\:{equation}\:{x}−{z}=\mathrm{4}\sqrt{\mathrm{3}}. \\ $$$${The}\:{line}\:{l}\:{has}\:{vector}\:{equation} \\ $$$$\boldsymbol{{r}}=\lambda\left[\left({cos}\theta+\sqrt{\mathrm{3}}\right)\boldsymbol{{i}}+\left(\sqrt{\mathrm{2}}{sin}\theta\right)\boldsymbol{{j}}+\left({cos}\theta−\sqrt{\mathrm{3}}\right)\boldsymbol{{k}}\right] \\ $$$${where}\:\lambda\:{is}\:{a}\:{scalar}\:{parameter}. \\ $$$${If}\:{l}\:{meets}\:{the}\:{plane}\:{at}\:{P},\:{show}\:{that}, \\ $$$${as}\:\theta\:{varies},\:{P}\:\:{describes}\:{a}\:{circle}.\: \\ $$ Answered by 123456…

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Question Number 132920 by liberty last updated on 17/Feb/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2sin}\:\mathrm{x}−\mathrm{sin}\:\mathrm{2x}}{\mathrm{x}−\mathrm{sin}\:\mathrm{x}} \\ $$ Answered by bobhans last updated on 17/Feb/21 $$\:{L}'{H}\ddot {{o}pital} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2cos}\:{x}−\mathrm{2cos}\:\mathrm{2}{x}}{\mathrm{1}−\mathrm{cos}\:{x}}\:=…

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Question Number 67382 by Mikael last updated on 26/Aug/19 $${calculate}\:{if}\:{there}\:{are}\:{maxims}\:{and}\:{minimus}\:{of} \\ $$$${the}\:{following}\:{function}: \\ $$$${y}=\begin{cases}{{x}^{\mathrm{2}} +\mathrm{1}\:{if}\:{x}\lneq\mathrm{1}}\\{−{x}+\mathrm{4}\:{if}\:{x}\geqslant\mathrm{1}}\end{cases} \\ $$ Commented by mr W last updated on 26/Aug/19…