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Question Number 105246    Answers: 4   Comments: 0

lim_(x→0) (cosx)^(1/x^2 )

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{cos}{x}\right)^{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }} \\ $$

Question Number 101730    Answers: 0   Comments: 3

Version 2.091 is available: - Slightly darker characters are used by default. A preference setting is available to revert to previous font. Change setting and restart app. - A new menu option mark as answered is added. This just mark as answered so that question will not show in unanswered question search.

$$\mathrm{Version}\:\mathrm{2}.\mathrm{091}\:\mathrm{is}\:\mathrm{available}: \\ $$$$-\:\mathrm{Slightly}\:\mathrm{darker}\:\mathrm{characters}\:\mathrm{are} \\ $$$$\:\:\:\:\mathrm{used}\:\mathrm{by}\:\mathrm{default}. \\ $$$$\:\:\:\:\mathrm{A}\:\mathrm{preference}\:\mathrm{setting}\:\mathrm{is}\:\mathrm{available} \\ $$$$\:\:\:\:\mathrm{to}\:\mathrm{revert}\:\mathrm{to}\:\mathrm{previous}\:\mathrm{font}. \\ $$$$\:\:\:\:\mathrm{Change}\:\mathrm{setting}\:\mathrm{and}\:\mathrm{restart}\:\mathrm{app}. \\ $$$$-\:\mathrm{A}\:\mathrm{new}\:\mathrm{menu}\:\mathrm{option}\:\mathrm{mark}\:\mathrm{as} \\ $$$$\:\:\:\mathrm{answered}\:\mathrm{is}\:\mathrm{added}.\:\mathrm{This}\:\mathrm{just}\:\mathrm{mark} \\ $$$$\:\:\:\mathrm{as}\:\mathrm{answered}\:\mathrm{so}\:\mathrm{that}\:\mathrm{question}\:\mathrm{will} \\ $$$$\:\:\:\mathrm{not}\:\mathrm{show}\:\mathrm{in}\:\mathrm{unanswered}\:\mathrm{question} \\ $$$$\:\:\:\mathrm{search}. \\ $$

Question Number 101693    Answers: 3   Comments: 2

There are 4 identical mathematics books, 2 identic physics books and 2 identical chemistry books . How many ways to compile the eight books on the condition of the same book are not mutually adjacent?

$$\mathrm{There}\:\mathrm{are}\:\mathrm{4}\:\mathrm{identical}\:\mathrm{mathematics} \\ $$$$\mathrm{books},\:\mathrm{2}\:\mathrm{identic}\:\mathrm{physics}\:\mathrm{books} \\ $$$$\mathrm{and}\:\mathrm{2}\:\mathrm{identical}\:\mathrm{chemistry}\:\mathrm{books} \\ $$$$.\:\mathrm{How}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{to}\:\mathrm{compile}\: \\ $$$$\mathrm{the}\:\mathrm{eight}\:\mathrm{books}\:\mathrm{on}\:\mathrm{the}\:\mathrm{condition} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{same}\:\mathrm{book}\:\mathrm{are}\:\mathrm{not}\:\mathrm{mutually} \\ $$$$\mathrm{adjacent}? \\ $$

Question Number 101686    Answers: 0   Comments: 5

Question Number 105306    Answers: 1   Comments: 1

(1/(2+(√2))) +(1/(3(√2)+2(√3) ))+(1/(4(√3)+3(√4)))+...+(1/(100(√(99))+99(√(100))))

$$\frac{\mathrm{1}}{\mathrm{2}+\sqrt{\mathrm{2}}}\:+\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}+\mathrm{2}\sqrt{\mathrm{3}}\:}+\frac{\mathrm{1}}{\mathrm{4}\sqrt{\mathrm{3}}+\mathrm{3}\sqrt{\mathrm{4}}}+...+\frac{\mathrm{1}}{\mathrm{100}\sqrt{\mathrm{99}}+\mathrm{99}\sqrt{\mathrm{100}}} \\ $$

Question Number 101680    Answers: 2   Comments: 0

Question Number 101671    Answers: 0   Comments: 0

What is the set of point M in each case: 1) ∣∣6MG^(→) ∣∣=∣∣−2GC^(→) ∣∣ 2) (6MG^(→) )×(−2GC^(→) )=0

$${What}\:{is}\:{the}\:{set}\:{of}\:{point}\:{M}\:{in}\:{each} \\ $$$${case}: \\ $$$$\left.\mathrm{1}\right)\:\:\:\:\mid\mid\mathrm{6}\overset{\rightarrow} {{MG}}\mid\mid=\mid\mid−\mathrm{2}\overset{\rightarrow} {{GC}}\mid\mid \\ $$$$\left.\mathrm{2}\right)\:\:\:\:\left(\mathrm{6}\overset{\rightarrow} {{MG}}\right)×\left(−\mathrm{2}\overset{\rightarrow} {{GC}}\right)=\mathrm{0} \\ $$

Question Number 105250    Answers: 1   Comments: 0

(1/(1×3))+(2/(1×3×5))+(3/(1×3×5×7))+.........n−terms Find sum

$$\frac{\mathrm{1}}{\mathrm{1}×\mathrm{3}}+\frac{\mathrm{2}}{\mathrm{1}×\mathrm{3}×\mathrm{5}}+\frac{\mathrm{3}}{\mathrm{1}×\mathrm{3}×\mathrm{5}×\mathrm{7}}+.........\mathrm{n}−\mathrm{terms} \\ $$$$\mathrm{Find}\:\mathrm{sum} \\ $$

Question Number 101650    Answers: 2   Comments: 1

Question Number 101658    Answers: 1   Comments: 0

solve in R x^3 −4x−1=0

$${solve}\:{in}\:\mathbb{R} \\ $$$${x}^{\mathrm{3}} −\mathrm{4}{x}−\mathrm{1}=\mathrm{0} \\ $$

Question Number 101645    Answers: 1   Comments: 0

E is a vectorial plane in B=(i^→ ,j^→ ) base. f is an endomorphism of E. f(i^→ )=4i^→ −j^→ and f(j^→ )=2i^→ +j^→ . u^→ =xi^→ +yj^→ ∈ E and x,y ∈ R. 1) Determinate f^( −1) (u).

$${E}\:{is}\:{a}\:{vectorial}\:{plane}\:{in}\:{B}=\left(\overset{\rightarrow} {{i}},\overset{\rightarrow} {{j}}\right) \\ $$$${base}.\:{f}\:{is}\:{an}\:{endomorphism}\:{of}\:{E}. \\ $$$${f}\left(\overset{\rightarrow} {{i}}\right)=\mathrm{4}\overset{\rightarrow} {{i}}−\overset{\rightarrow} {{j}}\:{and}\:{f}\left(\overset{\rightarrow} {{j}}\right)=\mathrm{2}\overset{\rightarrow} {{i}}+\overset{\rightarrow} {{j}}. \\ $$$$\overset{\rightarrow} {{u}}={x}\overset{\rightarrow} {{i}}+{y}\overset{\rightarrow} {{j}}\:\in\:{E}\:{and}\:{x},{y}\:\in\:\mathbb{R}. \\ $$$$\left.\mathrm{1}\right)\:{Determinate}\:{f}^{\:−\mathrm{1}} \left({u}\right). \\ $$

Question Number 101641    Answers: 0   Comments: 1

hello every one for any user here please stop saying (please help me or who can help me or who is intellegent or.......) just post your question and if we can help you we will do.

$${hello}\:{every}\:{one} \\ $$$${for}\:{any}\:{user}\:{here}\:{please}\:{stop}\:{saying} \\ $$$$\left({please}\:{help}\:{me}\:{or}\:{who}\:{can}\:{help}\:{me}\:{or}\right. \\ $$$$\left.{who}\:{is}\:{intellegent}\:{or}.......\right) \\ $$$${just}\:{post}\:{your}\:{question}\:{and}\:{if}\:{we}\:{can} \\ $$$${help}\:{you}\:{we}\:{will}\:{do}. \\ $$$$ \\ $$

Question Number 101633    Answers: 1   Comments: 2

∫x^x^x ∙x^x ∙x dx=?

$$\int\mathrm{x}^{\mathrm{x}^{\mathrm{x}} } \centerdot\mathrm{x}^{\mathrm{x}} \centerdot\mathrm{x}\:\mathrm{dx}=? \\ $$

Question Number 101625    Answers: 0   Comments: 1

Question Number 101615    Answers: 3   Comments: 4

Question Number 101616    Answers: 2   Comments: 1

Question Number 101610    Answers: 2   Comments: 0

Question Number 101608    Answers: 0   Comments: 0

∫_(0 ) ^(π/2) ln(((ln^2 (sin(θ)))/(π^2 +ln^2 (sin(θ)))))((ln(cos(θ)))/(tan(θ)))dθ

$$\int_{\mathrm{0}\:} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\frac{{ln}^{\mathrm{2}} \left({sin}\left(\theta\right)\right)}{\pi^{\mathrm{2}} +{ln}^{\mathrm{2}} \left({sin}\left(\theta\right)\right)}\right)\frac{{ln}\left({cos}\left(\theta\right)\right)}{{tan}\left(\theta\right)}{d}\theta \\ $$

Question Number 101607    Answers: 0   Comments: 0

f(x)=(√(2x+7))+log_3 x f^(−1) (x)=?

$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{2x}+\mathrm{7}}+\mathrm{log}_{\mathrm{3}} \mathrm{x} \\ $$$$\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)=?\:\:\:\:\:\: \\ $$

Question Number 101601    Answers: 1   Comments: 0

∫_((√2)−1) ^((√2)+1) ((x^4 +x^2 +1)/((x^2 +1)^2 ))dx

$$\int_{\sqrt{\mathrm{2}}−\mathrm{1}} ^{\sqrt{\mathrm{2}}+\mathrm{1}} \frac{{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 101597    Answers: 0   Comments: 3

∫ ln (1+ e^x ) dx = ..

$$\:\int\:\mathrm{ln}\:\left(\mathrm{1}+\:{e}^{{x}} \right)\:{dx}\:=\:.. \\ $$

Question Number 101595    Answers: 2   Comments: 0

let f(x) =cos^n x 1) find f^((n)) (x) and f^((n)) (0) 2) developp f at integr serie 3) detemine ∫ f(x)dx

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{cos}^{\mathrm{n}} \mathrm{x} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{find}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{detemine}\:\:\int\:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 101585    Answers: 1   Comments: 0

∫_0 ^π (1/(a^2 −2a cosx + 1))dx (a<1) is

$$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{1}}{{a}^{\mathrm{2}} −\mathrm{2}{a}\:{cosx}\:+\:\mathrm{1}}{dx}\:\left({a}<\mathrm{1}\right)\:{is} \\ $$$$ \\ $$

Question Number 101582    Answers: 2   Comments: 0

lim_(n→∞) (1/n^2 ) Σ_(r=1) ^n r e^(r/n) =

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\:{r}\:{e}^{{r}/{n}} \:= \\ $$

Question Number 101590    Answers: 2   Comments: 1

p(2x+5)=(2x^2 +3x−1)Q(x+1) if Q(−1)=3 then p(1)=?

$$\mathrm{p}\left(\mathrm{2x}+\mathrm{5}\right)=\left(\mathrm{2x}^{\mathrm{2}} +\mathrm{3x}−\mathrm{1}\right)\mathrm{Q}\left(\mathrm{x}+\mathrm{1}\right) \\ $$$$\mathrm{if}\:\mathrm{Q}\left(−\mathrm{1}\right)=\mathrm{3}\:\:\:\:\:\mathrm{then}\:\mathrm{p}\left(\mathrm{1}\right)=? \\ $$

Question Number 101589    Answers: 1   Comments: 0

if sin10^0 =x then sin70^0 =?

$$\mathrm{if}\:\mathrm{sin10}^{\mathrm{0}} =\mathrm{x}\:\:\:\:\:\:\:\:\:\:\mathrm{then}\:\:\:\mathrm{sin70}^{\mathrm{0}} =? \\ $$

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