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Author: Tinku Tara

lets-f-R-R-and-g-Z-R-such-that-f-x-g-x-x-Z-given-a-Z-then-proof-or-give-a-counter-example-that-lim-x-a-f-x-g-a-

Question Number 1192 by 123456 last updated on 13/Jul/15 $$\mathrm{lets}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{and}\:{g}:\mathbb{Z}\rightarrow\mathbb{R}\:\mathrm{such}\:\mathrm{that} \\ $$$${f}\left({x}\right)={g}\left({x}\right),{x}\in\mathbb{Z} \\ $$$$\mathrm{given}\:{a}\in\mathbb{Z},\:\mathrm{then}\:\mathrm{proof}\:\mathrm{or}\:\mathrm{give}\:\mathrm{a}\:\mathrm{counter}\:\mathrm{example}\:\mathrm{that} \\ $$$$\underset{{x}\rightarrow{a}} {\mathrm{lim}}{f}\left({x}\right)={g}\left({a}\right) \\ $$ Commented by prakash jain last updated…

Question-132261

Question Number 132261 by muneer0o0 last updated on 12/Feb/21 Answered by Olaf last updated on 13/Feb/21 $$\Omega\:=\:\int_{−\mathrm{1}} ^{+\mathrm{1}} \int_{−\sqrt{\mathrm{1}−{y}^{\mathrm{2}} }} ^{+\sqrt{\mathrm{1}−{y}^{\mathrm{2}} }} \mathrm{sec}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){dxdy}…

Question-132260

Question Number 132260 by Salman_Abir last updated on 12/Feb/21 Answered by Olaf last updated on 13/Feb/21 $$\left({x}\sqrt{{x}}\right)^{{x}} \:=\:{x}^{{x}\sqrt{{x}}} \\ $$$$\left({x}^{\mathrm{3}/\mathrm{2}} \right)^{{x}} \:=\:{x}^{{x}^{\mathrm{3}/\mathrm{2}} } \\ $$$${x}\mathrm{ln}{x}^{\mathrm{3}/\mathrm{2}}…

Question-132257

Question Number 132257 by Salman_Abir last updated on 12/Feb/21 Answered by bemath last updated on 12/Feb/21 $$\left(\mathrm{i}\right)\mathrm{E}\left(\mathrm{0},\mathrm{0},\mathrm{8}\right),\:\mathrm{C}\left(\mathrm{3},\mathrm{3},\mathrm{0}\right)\:\mathrm{vector}\: \\ $$$$\:\mathrm{EC}\:=\:\mathrm{3}\hat {\mathrm{i}}+\mathrm{3}\hat {\mathrm{j}}−\mathrm{8}\hat {\mathrm{k}}\:;\:\mid\mathrm{EC}\mid=\sqrt{\mathrm{9}+\mathrm{9}+\mathrm{64}}\:=\sqrt{\mathrm{82}} \\ $$$$\:\mathrm{H}\left(\mathrm{0},\mathrm{3},\mathrm{8}\right)\:,\mathrm{B}\left(\mathrm{3},\mathrm{0},\mathrm{0}\right)\:\mathrm{vector}\: \\…

A-rectangular-glass-block-n-1-52-is-placed-inside-a-clean-water-contained-in-a-basin-A-layer-of-oil-n-1-44-floats-on-the-water-surface-A-ray-of-light-from-air-strikes-the-oil-surface-at-an-an

Question Number 132252 by aurpeyz last updated on 12/Feb/21 $$ \\ $$$$\mathrm{A}\:\mathrm{rectangular}\:\mathrm{glass}\:\mathrm{block}\:\left(\mathrm{n}=\mathrm{1}.\mathrm{52}\right)\:\mathrm{is} \\ $$$$\mathrm{pla}{c}\mathrm{ed}\:\mathrm{inside}\:\mathrm{a}\:\mathrm{clean}\:\mathrm{water}\:\mathrm{contained}\: \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{basin}.\:\mathrm{A}\:\mathrm{layer}\:\mathrm{of}\:\mathrm{oil}\:\left(\mathrm{n}=\mathrm{1}.\mathrm{44}\right)\:\mathrm{floats} \\ $$$$\mathrm{o}{n}\:\mathrm{the}\:\mathrm{water}\:\mathrm{surface}.\:\mathrm{A}\:\mathrm{ray}\:\mathrm{of}\:\mathrm{light}\: \\ $$$$\mathrm{from}\:\mathrm{air}\:\mathrm{strikes}\:\mathrm{the}\:\mathrm{oil}\:\mathrm{surface}\:\mathrm{at}\:\mathrm{an} \\ $$$$\mathrm{ange}\:\mathrm{of}\:\mathrm{incidence}\:\mathrm{of}\:\mathrm{28}^{\mathrm{0}} .\:\mathrm{Calculate}\:\mathrm{the} \\ $$$$\mathrm{a}{n}\mathrm{gle}\:\mathrm{of}\:\mathrm{refraction}\:\mathrm{at}\:\mathrm{the}\:\mathrm{water}−\mathrm{glass}…

A-ray-of-light-is-incident-at-60-0-at-an-air-glass-plane-surface-find-the-angle-of-refraction-in-the-glass-refractive-index-for-glass-1-5-a-25-3-b-35-3-c-15-3-d-30-

Question Number 132255 by aurpeyz last updated on 12/Feb/21 $${A}\:{ray}\:{of}\:{light}\:{is}\:{incident}\:{at}\:\mathrm{60}^{\mathrm{0}} \:{at}\:{an} \\ $$$${air}−{glass}\:{plane}\:{surface}.\:{find}\:{the}\: \\ $$$${angle}\:{of}\:{refraction}\:{in}\:{the}\:{glass}\left(\right. \\ $$$$\left.{refractive}\:{index}\:{for}\:{glass}=\mathrm{1}.\mathrm{5}\right) \\ $$$$\left({a}\right)\:\mathrm{25}.\mathrm{3}\:\left({b}\right)\:\mathrm{35}.\mathrm{3}\:\left({c}\right)\:\mathrm{15}.\mathrm{3}\:\left({d}\right)\mathrm{30} \\ $$ Commented by Dwaipayan Shikari…