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AllQuestion and Answers: Page 257

Question Number 195996 Answers: 2 Comments: 0

Question Number 195982 Answers: 2 Comments: 0

lim_(x→1) [(1/(2(1−(√x))))−(1/(3(1−(x)^(1/3) )))]=? with out l′pital rule

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\left[\frac{\mathrm{1}}{\mathrm{2}\left(\mathrm{1}−\sqrt{{x}}\right)}−\frac{\mathrm{1}}{\mathrm{3}\left(\mathrm{1}−\sqrt[{\mathrm{3}}]{{x}}\right)}\right]=? \\ $$$${with}\:{out}\:{l}'{pital}\:{rule} \\ $$

Question Number 196026 Answers: 1 Comments: 0

∫^( +∞) _( 0) (((lnt)^2 )/(1+t^2 ))dt

$$\underset{\:\mathrm{0}} {\int}^{\:+\infty} \frac{\left({lnt}\right)^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$

Question Number 195964 Answers: 1 Comments: 0

the family A has 5 members and the family B has 4 members. there are 6 personsfrom other families. in how many ways can you arrange these 15 persons around a round table such that no member from family A and no member from family B are next to each other?

$${the}\:{family}\:{A}\:{has}\:\mathrm{5}\:{members}\:{and}\:{the} \\ $$$${family}\:{B}\:{has}\:\mathrm{4}\:{members}.\:{there}\:{are}\: \\ $$$$\mathrm{6}\:{personsfrom}\:{other}\:{families}. \\ $$$${in}\:{how}\:{many}\:{ways}\:{can}\:{you}\:{arrange} \\ $$$${these}\:\mathrm{15}\:{persons}\:{around}\:{a}\:{round}\:{table} \\ $$$${such}\:{that}\:{no}\:{member}\:{from}\:{family}\:{A} \\ $$$${and}\:{no}\:{member}\:{from}\:{family}\:{B}\:{are} \\ $$$${next}\:{to}\:{each}\:{other}? \\ $$

Question Number 195972 Answers: 0 Comments: 0

Question Number 195971 Answers: 3 Comments: 0

if f′(x)=((f(x+a)−f(x))/a), find f(x).

$${if}\:{f}'\left({x}\right)=\frac{{f}\left({x}+{a}\right)−{f}\left({x}\right)}{{a}},\:{find}\:{f}\left({x}\right). \\ $$

Question Number 195973 Answers: 0 Comments: 0

Question Number 195954 Answers: 3 Comments: 0

Question Number 195953 Answers: 0 Comments: 0

Question Number 195952 Answers: 2 Comments: 0

Ω = Σ_(m=1) ^∞ Σ_(n=1) ^∞ (((−1)^( n+1) )/(m^2 n + mn^( 2) )) = ? −−−−−

$$ \\ $$$$\:\:\:\:\Omega\:=\:\underset{{m}=\mathrm{1}} {\overset{\infty} {\sum}}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{\:{n}+\mathrm{1}} }{{m}^{\mathrm{2}} {n}\:+\:{mn}^{\:\mathrm{2}} }\:\:=\:?\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:−−−−− \\ $$

Question Number 195948 Answers: 0 Comments: 0

An object is said to cross a thousand kilimeters in planks constant. How many times faster is the object to the speed of light. plank′s time = 10^(−44) sec.

$$\mathrm{An}\:\mathrm{object}\:\mathrm{is}\:\mathrm{said}\:\mathrm{to}\:\mathrm{cross}\:\mathrm{a}\:\mathrm{thousand}\: \\ $$$$\mathrm{kilimeters}\:\mathrm{in}\:\mathrm{planks}\:\mathrm{constant}.\:\mathrm{How}\:\mathrm{many} \\ $$$$\mathrm{times}\:\mathrm{faster}\:\mathrm{is}\:\mathrm{the}\:\mathrm{object}\:\mathrm{to}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of} \\ $$$$\mathrm{light}.\:\mathrm{plank}'\mathrm{s}\:\mathrm{time}\:=\:\mathrm{10}^{−\mathrm{44}} \mathrm{sec}. \\ $$

Question Number 195947 Answers: 2 Comments: 0

Question Number 195944 Answers: 1 Comments: 0

Question Number 195911 Answers: 0 Comments: 0

Question Number 195910 Answers: 1 Comments: 0

Question Number 195905 Answers: 1 Comments: 0

lim_(x→0) (((√(3+x^4 )) −(√(3+tan^4 x)))/x^6 ) =?

$$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{3}+\mathrm{x}^{\mathrm{4}} }\:−\sqrt{\mathrm{3}+\mathrm{tan}\:^{\mathrm{4}} \mathrm{x}}}{\mathrm{x}^{\mathrm{6}} }\:=? \\ $$

Question Number 195904 Answers: 1 Comments: 0

Σ_(n=0) ^∞ [((2^n (2n)!)/(3^(2n+1) (n+1)!n!))]=λ Evaluate (λ)

$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left[\frac{\mathrm{2}^{{n}} \left(\mathrm{2}{n}\right)!}{\mathrm{3}^{\mathrm{2}{n}+\mathrm{1}} \left({n}+\mathrm{1}\right)!{n}!}\right]=\lambda \\ $$$${Evaluate}\:\left(\lambda\right) \\ $$

Question Number 195931 Answers: 1 Comments: 2

Question Number 195900 Answers: 1 Comments: 0

Question Number 195898 Answers: 1 Comments: 0

Question Number 195896 Answers: 2 Comments: 0

Question Number 195895 Answers: 1 Comments: 0

Calcul ∫^( (π/2)) _( 0) t(√(tan(t))) dt

$$\mathrm{Calcul}\:\:\:\:\:\:\:\:\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \mathrm{t}\sqrt{\mathrm{tan}\left(\mathrm{t}\right)}\:\mathrm{dt} \\ $$

Question Number 195892 Answers: 1 Comments: 0

Question Number 195885 Answers: 2 Comments: 0

(dy/dx) + (√((1−y^2 )/(1−x^2 ))) = 0

$$\:\:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\sqrt{\frac{\mathrm{1}−\mathrm{y}^{\mathrm{2}} }{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:=\:\mathrm{0}\: \\ $$

Question Number 195884 Answers: 0 Comments: 0

solve the integral by the method of Differentiation ∫_0 ^1 ((x^2 −1)/(log_2 (x)))dx

$$\mathrm{solve}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{by}\:\mathrm{the}\:\mathrm{method}\: \\ $$$$\mathrm{of}\:\mathrm{Differentiation} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}{\mathrm{log}_{\mathrm{2}} \left(\mathrm{x}\right)}\mathrm{dx} \\ $$

Question Number 195883 Answers: 0 Comments: 0

The speed of a boat is given by, V=k((l/t)−at), where k is the constant and l is the distance travel by boat in time t and a is the acceleration of water. If there is a change in l from 2cm to 1cm in time 2sec. to 1sec. If the acceleration of water changes from 0.95m/s^2 to 2m/s^2 . Find the motion of boat.

$$\mathrm{The}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{a}\:\mathrm{boat}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by},\:\mathrm{V}=\mathrm{k}\left(\frac{\mathrm{l}}{\mathrm{t}}−\mathrm{at}\right), \\ $$$$\mathrm{where}\:\mathrm{k}\:\mathrm{is}\:\mathrm{the}\:\mathrm{constant}\:\mathrm{and}\:\mathrm{l}\:\mathrm{is}\:\mathrm{the}\:\mathrm{distance} \\ $$$$\mathrm{travel}\:\mathrm{by}\:\mathrm{boat}\:\mathrm{in}\:\mathrm{time}\:\mathrm{t}\:\mathrm{and}\:\mathrm{a}\:\mathrm{is}\:\mathrm{the}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{water}.\: \\ $$$$\mathrm{If}\:\mathrm{there}\:\mathrm{is}\:\mathrm{a}\:\mathrm{change}\:\mathrm{in}\:\mathrm{l}\:\mathrm{from}\:\mathrm{2cm}\:\mathrm{to}\:\mathrm{1cm}\:\mathrm{in}\:\mathrm{time}\:\mathrm{2sec}.\:\mathrm{to}\:\mathrm{1sec}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{acceleration} \\ $$$$\mathrm{of}\:\mathrm{water}\:\mathrm{changes}\:\mathrm{from}\:\mathrm{0}.\mathrm{95m}/\mathrm{s}^{\mathrm{2}} \:\mathrm{to}\:\mathrm{2m}/\mathrm{s}^{\mathrm{2}} .\:\mathrm{Find}\:\mathrm{the}\:\mathrm{motion}\:\mathrm{of}\:\mathrm{boat}. \\ $$

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