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Question Number 92032 Answers: 0 Comments: 0

lim_(x→∞) ((2^(4n−1) ∗(n!)^2 )/((2n+1)∗[2n p(n)]^2 ))

$$\underset{{x}\rightarrow\infty} {{lim}}\frac{\mathrm{2}^{\mathrm{4}{n}−\mathrm{1}} \ast\left({n}!\right)^{\mathrm{2}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)\ast\left[\mathrm{2}{n}\:{p}\left({n}\right)\right]^{\mathrm{2}} } \\ $$

Question Number 92016 Answers: 1 Comments: 0

Question Number 92013 Answers: 1 Comments: 10

Solve: 2^x + 3^y = 72 ..... (i) 2^y + 3^x = 108 ..... (ii)

$$\mathrm{Solve}: \\ $$$$\:\:\:\mathrm{2}^{\mathrm{x}} \:\:+\:\:\mathrm{3}^{\mathrm{y}} \:\:\:=\:\:\mathrm{72}\:\:\:\:\:.....\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\mathrm{2}^{\mathrm{y}} \:\:+\:\:\mathrm{3}^{\mathrm{x}} \:\:\:=\:\:\mathrm{108}\:\:\:\:\:.....\:\left(\mathrm{ii}\right) \\ $$

Question Number 92010 Answers: 1 Comments: 0

if log_6 30 = a and log_(24) 15 = b log_(12) 60 = ?

$$\mathrm{if}\:\mathrm{log}_{\mathrm{6}} \mathrm{30}\:=\:{a}\:\mathrm{and}\:\mathrm{log}_{\mathrm{24}} \mathrm{15}\:=\:{b} \\ $$$$\mathrm{log}_{\mathrm{12}} \mathrm{60}\:=\:? \\ $$

Question Number 92008 Answers: 0 Comments: 1

Sum of infinite series: 1 + (3/4) + ((3.5)/(4.8)) + ((3.5.7)/(4.8.12)) + ... is ?

$$\mathrm{Sum}\:\mathrm{of}\:\mathrm{infinite}\:\mathrm{series}:\:\:\mathrm{1}\:\:+\:\:\frac{\mathrm{3}}{\mathrm{4}}\:\:+\:\:\frac{\mathrm{3}.\mathrm{5}}{\mathrm{4}.\mathrm{8}}\:\:+\:\:\frac{\mathrm{3}.\mathrm{5}.\mathrm{7}}{\mathrm{4}.\mathrm{8}.\mathrm{12}}\:\:+\:\:...\:\:\:\:\mathrm{is}\:? \\ $$

Question Number 92003 Answers: 0 Comments: 2

The sum to n terms of the series (3/1^2 ) + (5/(1^2 +2^2 )) + (7/(1^2 +2^2 +3^2 )) + .... is

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{to}\:{n}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series} \\ $$$$\frac{\mathrm{3}}{\mathrm{1}^{\mathrm{2}} }\:+\:\frac{\mathrm{5}}{\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} }\:+\:\frac{\mathrm{7}}{\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} }\:+\:....\:\mathrm{is} \\ $$

Question Number 91996 Answers: 0 Comments: 2

∫(arcsinx)^2 dx=?

$$\int\left(\mathrm{arcsinx}\right)^{\mathrm{2}} \mathrm{dx}=? \\ $$

Question Number 91995 Answers: 0 Comments: 1

hello what is the metric of schwarzchild dynamics.

$${hello}\:{what}\:{is}\:{the}\:{metric}\:{of}\:{schwarzchild}\:{dynamics}. \\ $$

Question Number 92025 Answers: 2 Comments: 1

∫(((x−1)/(x^2 −x−1)))dx

$$\int\left(\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}^{\mathrm{2}} −\mathrm{x}−\mathrm{1}}\right)\mathrm{dx} \\ $$

Question Number 91977 Answers: 4 Comments: 10

Question Number 91982 Answers: 0 Comments: 0

show that ∫_0 ^(π/2) csc(x) tan^(−1) (sin(x)) dx=(π/2)ln(1+(√2))

$${show}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {csc}\left({x}\right)\:{tan}^{−\mathrm{1}} \left({sin}\left({x}\right)\right)\:{dx}=\frac{\pi}{\mathrm{2}}{ln}\left(\mathrm{1}+\sqrt{\mathrm{2}}\right) \\ $$

Question Number 91990 Answers: 0 Comments: 2

Question Number 92000 Answers: 1 Comments: 0

proof 0!!=1

$$\mathrm{proof}\:\mathrm{0}!!=\mathrm{1} \\ $$

Question Number 91961 Answers: 0 Comments: 1

∫ cos^3 (2x) sin^3 (3x) dx

$$\int\:\mathrm{cos}\:^{\mathrm{3}} \left(\mathrm{2x}\right)\:\mathrm{sin}\:^{\mathrm{3}} \left(\mathrm{3x}\right)\:\mathrm{dx}\: \\ $$

Question Number 91960 Answers: 0 Comments: 3

If f(x) is an even function is Σ_(n=−∞) ^∞ f(n)=2Σ_(n=0) ^∞ f(n) true?

$$\mathrm{If} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{an}\:{e}\mathrm{ven}\:\mathrm{function}\:\mathrm{is} \\ $$$$\underset{{n}=−\infty} {\overset{\infty} {\sum}}{f}\left({n}\right)=\mathrm{2}\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}{f}\left({n}\right)\:{true}? \\ $$

Question Number 91954 Answers: 0 Comments: 4

lim_(x→0^+ ) ((ln(sin 2x))/(ln(sin 4x)))

$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\mathrm{ln}\left(\mathrm{sin}\:\mathrm{2x}\right)}{\mathrm{ln}\left(\mathrm{sin}\:\mathrm{4x}\right)} \\ $$

Question Number 91948 Answers: 0 Comments: 1

Question Number 91946 Answers: 2 Comments: 3

a particle is projected from a point at a height 3h metres above a horizontal play ground. the direction of the projectile makes an angle α with the horizontal through the point of projection. show that if th greatest height reached above the point lc projection is h metres, then the horizontal distance travelled by the particle before striking the plane is 6h cotα metres. Find the vertical and horizontal component of the speed of the particle just before it hits the ground.

$$\mathrm{a}\:\mathrm{particle}\:\mathrm{is}\:\mathrm{projected}\:\mathrm{from}\:\mathrm{a}\:\mathrm{point}\:\mathrm{at}\:\mathrm{a}\:\mathrm{height}\:\mathrm{3}{h}\:\mathrm{metres}\:\mathrm{above}\:\mathrm{a}\:\mathrm{horizontal} \\ $$$$\mathrm{play}\:\mathrm{ground}.\:\mathrm{the}\:\mathrm{direction}\:\mathrm{of}\:\mathrm{the}\:\mathrm{projectile}\:\mathrm{makes}\:\mathrm{an}\:\mathrm{angle}\:\alpha\:\mathrm{with}\:\mathrm{the} \\ $$$$\mathrm{horizontal}\:\mathrm{through}\:\mathrm{the}\:\mathrm{point}\:\mathrm{of}\:\mathrm{projection}.\:\:\mathrm{show}\:\mathrm{that}\:\mathrm{if}\:\mathrm{th}\:\mathrm{greatest} \\ $$$$\mathrm{height}\:\mathrm{reached}\:\mathrm{above}\:\mathrm{the}\:\mathrm{point}\:\mathrm{lc}\:\mathrm{projection}\:\mathrm{is}\:{h}\:\mathrm{metres},\:\mathrm{then}\:\mathrm{the}\:\mathrm{horizontal} \\ $$$$\mathrm{distance}\:\mathrm{travelled}\:\mathrm{by}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{before}\:\mathrm{striking}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{is}\:\mathrm{6}{h}\:\mathrm{cot}\alpha\:\mathrm{metres}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{vertical}\:\mathrm{and}\:\mathrm{horizontal}\:\mathrm{component}\:\mathrm{of}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{just} \\ $$$$\mathrm{before}\:\mathrm{it}\:\mathrm{hits}\:\mathrm{the}\:\mathrm{ground}. \\ $$

Question Number 91933 Answers: 1 Comments: 2

Question Number 91936 Answers: 0 Comments: 6

how to evaluate ln(i), i=(√(−1)).

$${how}\:{to}\:{evaluate}\:{ln}\left({i}\right),\:{i}=\sqrt{−\mathrm{1}}. \\ $$

Question Number 91931 Answers: 0 Comments: 3

∫_0 ^1 ln(Γ(x)) dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\Gamma\left({x}\right)\right)\:{dx} \\ $$

Question Number 91930 Answers: 0 Comments: 2

lim_(x→0) cos (1/x)=

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}cos}\:\frac{\mathrm{1}}{{x}}= \\ $$

Question Number 91919 Answers: 0 Comments: 1

The value of sin 12° sin 48° sin 54° is

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{sin}\:\mathrm{12}°\:\mathrm{sin}\:\mathrm{48}°\:\mathrm{sin}\:\mathrm{54}°\:\:\mathrm{is} \\ $$

Question Number 91914 Answers: 1 Comments: 0

hi every one here i will put my solution for old question by mr.MJS ∫((√((x−1)x(x+1)))/(3x^2 −4))dx the solution by using Appell hypergeometric function

$${hi}\:{every}\:{one}\:{here}\:{i}\:{will}\:{put}\:{my}\:{solution}\:\: \\ $$$${for}\:{old}\:{question}\:{by}\:{mr}.{MJS} \\ $$$$\int\frac{\sqrt{\left({x}−\mathrm{1}\right){x}\left({x}+\mathrm{1}\right)}}{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{4}}{dx} \\ $$$$ \\ $$$${the}\:{solution}\:{by}\:{using}\:\:\: \\ $$$${Appell}\:{hypergeometric}\:{function} \\ $$

Question Number 91912 Answers: 0 Comments: 2

if ∣x∣, ∣x−1∣, ∣x+1∣ are first three terms of an AP. then what is the sum of it′s first 10 terms equal to

$$\mathrm{if}\:\mid\mathrm{x}\mid,\:\mid\mathrm{x}−\mathrm{1}\mid,\:\mid\mathrm{x}+\mathrm{1}\mid\:\mathrm{are}\:\mathrm{first} \\ $$$$\mathrm{three}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{AP}.\:\mathrm{then}\: \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{it}'\mathrm{s}\:\mathrm{first} \\ $$$$\mathrm{10}\:\mathrm{terms}\:\mathrm{equal}\:\mathrm{to}\: \\ $$

Question Number 91911 Answers: 1 Comments: 0

y′′′′+2y′′+y=sin x

$$\mathrm{y}''''+\mathrm{2y}''+\mathrm{y}=\mathrm{sin}\:\mathrm{x}\: \\ $$

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