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Question Number 140090 Answers: 2 Comments: 0

(1/2^1 )+(3/2^3 )+(5/2^5 )+(7/2^7 )+..=?

$$\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{1}} }+\frac{\mathrm{3}}{\mathrm{2}^{\mathrm{3}} }+\frac{\mathrm{5}}{\mathrm{2}^{\mathrm{5}} }+\frac{\mathrm{7}}{\mathrm{2}^{\mathrm{7}} }+..=? \\ $$

Question Number 140089 Answers: 1 Comments: 0

Given that log_4 (y−1)+log_4 ((x/y))=k and log_2 (y+1)−log_2 x=k−1 Show that y^2 =1+8^k Hence deduce the value of y and x when k=1

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{log}_{\mathrm{4}} \left(\mathrm{y}−\mathrm{1}\right)+\mathrm{log}_{\mathrm{4}} \left(\frac{\mathrm{x}}{\mathrm{y}}\right)=\mathrm{k} \\ $$$$\mathrm{and}\:\mathrm{log}_{\mathrm{2}} \left(\mathrm{y}+\mathrm{1}\right)−\mathrm{log}_{\mathrm{2}} \mathrm{x}=\mathrm{k}−\mathrm{1} \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{y}^{\mathrm{2}} =\mathrm{1}+\mathrm{8}^{\mathrm{k}} \\ $$$$\mathrm{Hence}\:\mathrm{deduce}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{y}\:\mathrm{and}\:\mathrm{x}\: \\ $$$$\mathrm{when}\:\mathrm{k}=\mathrm{1} \\ $$

Question Number 140086 Answers: 0 Comments: 0

Q136005

$${Q}\mathrm{136005} \\ $$

Question Number 140076 Answers: 2 Comments: 6

Question Number 140075 Answers: 0 Comments: 0

if z=(x^2 /y)+3y find the absolute and relative error ?

$${if}\:{z}=\frac{{x}^{\mathrm{2}} }{{y}}+\mathrm{3}{y}\:\:\:{find}\:{the}\:{absolute}\:{and}\:{relative} \\ $$$${error}\:? \\ $$

Question Number 140073 Answers: 1 Comments: 0

Let f(x)= { ((3x^2 −1 ; x<0)),((cx+d ; 0≤x≤1)),(((√(x+8)) ; x>1)) :} find the value of c & d such that f(x) continous everywhere

$$\mathrm{Let}\:\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\mathrm{3x}^{\mathrm{2}} −\mathrm{1}\:;\:\mathrm{x}<\mathrm{0}}\\{\mathrm{cx}+\mathrm{d}\:;\:\mathrm{0}\leqslant\mathrm{x}\leqslant\mathrm{1}}\\{\sqrt{\mathrm{x}+\mathrm{8}}\:;\:\mathrm{x}>\mathrm{1}}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{c}\:\&\:\mathrm{d}\:\mathrm{such}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{continous} \\ $$$$\mathrm{everywhere} \\ $$

Question Number 140071 Answers: 1 Comments: 0

For what value of k is the following continous function ? f(x)= { (((((√(7x+2))−(√(6x+4)))/(x−2)) ; if x≥−(2/7) & x≠2)),(( k ; if x=2)) :}

$$\mathrm{For}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:\mathrm{k}\:\mathrm{is}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{continous}\:\mathrm{function}\:? \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\frac{\sqrt{\mathrm{7x}+\mathrm{2}}−\sqrt{\mathrm{6x}+\mathrm{4}}}{\mathrm{x}−\mathrm{2}}\:;\:\mathrm{if}\:\mathrm{x}\geqslant−\frac{\mathrm{2}}{\mathrm{7}}\:\&\:\mathrm{x}\neq\mathrm{2}}\\{\:\:\:\:\:\:\:\:\mathrm{k}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:;\:\mathrm{if}\:\mathrm{x}=\mathrm{2}}\end{cases} \\ $$

Question Number 140064 Answers: 0 Comments: 0

Question Number 140057 Answers: 0 Comments: 0

Question Number 140056 Answers: 2 Comments: 0

Prove the folowing result: ∫_0 ^(π/2) cot θ∙(log sec θ)^3 dθ=(π^4 /(240)) . I need your help, if possible please.

$$\mathrm{Prove}\:\mathrm{the}\:\mathrm{folowing}\:\mathrm{result}: \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{cot}\:\theta\centerdot\left(\mathrm{log}\:\mathrm{sec}\:\theta\right)^{\mathrm{3}} {d}\theta=\frac{\pi^{\mathrm{4}} }{\mathrm{240}} \\ $$$$. \\ $$$$\mathrm{I}\:\mathrm{need}\:\mathrm{your}\:\mathrm{help},\:\mathrm{if}\:\mathrm{possible}\:\mathrm{please}. \\ $$

Question Number 140055 Answers: 2 Comments: 0

prove that : Ω:= ∫_0 ^( ∞) ((1−e^(−x) )/(1+e^(2x) )) .(dx/x) =ln(((Γ^2 ((1/4)))/(4(√(2π)))) ) Θ:= Π_(n=1) ^∞ (((2n+1)/(2n)))^((−1)^(n+1) ) =^(??) e^Ω

$$\:\:\:\:\:\: \\ $$$$\:\:{prove}\:\:{that}\:: \\ $$$$\:\:\:\:\:\:\:\:\Omega:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{1}−{e}^{−{x}} }{\mathrm{1}+{e}^{\mathrm{2}{x}} }\:.\frac{{dx}}{{x}}\:={ln}\left(\frac{\Gamma^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)}{\mathrm{4}\sqrt{\mathrm{2}\pi}}\:\right) \\ $$$$\:\Theta:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\frac{\mathrm{2}{n}+\mathrm{1}}{\mathrm{2}{n}}\right)^{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} } \overset{??} {=}\:{e}^{\Omega} \\ $$$$\:\:\:\:\:\:\: \\ $$

Question Number 140053 Answers: 0 Comments: 3

Question Number 140050 Answers: 3 Comments: 0

prove that:: φ :=lim_(n→∞) (n/( (√(2k)))) .(√(1−cos^k (((2π)/n)))) =π ................

$$\:\:\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\:\:\:\:\phi\::={lim}_{{n}\rightarrow\infty} \frac{{n}}{\:\sqrt{\mathrm{2}{k}}}\:.\sqrt{\mathrm{1}−{cos}^{{k}} \left(\frac{\mathrm{2}\pi}{{n}}\right)}\:=\pi \\ $$$$\:\:\:\:\:\:\:\:................ \\ $$$$ \\ $$

Question Number 140738 Answers: 0 Comments: 4

Question Number 140046 Answers: 2 Comments: 1

........... nice .......calculus(I) ........ Θ :=lim_( x→ (π/4)) ( tan(x) )^( tan(2x)) =? ...............................

$$\:\:\:\:\:\:\:\:\:\:...........\:{nice}\:.......{calculus}\left({I}\right)\:........ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Theta\::={lim}_{\:{x}\rightarrow\:\frac{\pi}{\mathrm{4}}} \:\left(\:{tan}\left({x}\right)\:\right)^{\:{tan}\left(\mathrm{2}{x}\right)} \:=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:............................... \\ $$$$ \\ $$

Question Number 140042 Answers: 1 Comments: 0

Question Number 140040 Answers: 3 Comments: 0

((45+29(√2)))^(1/3) + ((45−29(√2)))^(1/3) =?

$$\:\sqrt[{\mathrm{3}}]{\mathrm{45}+\mathrm{29}\sqrt{\mathrm{2}}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{45}−\mathrm{29}\sqrt{\mathrm{2}}}\:=?\: \\ $$

Question Number 140030 Answers: 1 Comments: 0

Question Number 140029 Answers: 1 Comments: 0

si p=ab and (a=1 ou b=1) then p is prime?

$${si}\:{p}={ab}\:{and}\:\left({a}=\mathrm{1}\:{ou}\:{b}=\mathrm{1}\right)\:{then}\:{p}\:{is}\:{prime}? \\ $$

Question Number 140028 Answers: 0 Comments: 0

Evaluate ::: P :=Π_(k=3) ^∞ (((k^3 +3k)^2 )/(k^6 −64))=? ..........................

$$\:\:\:{Evaluate}\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{P}\::=\underset{{k}=\mathrm{3}} {\overset{\infty} {\prod}}\frac{\left({k}^{\mathrm{3}} +\mathrm{3}{k}\right)^{\mathrm{2}} }{{k}^{\mathrm{6}} −\mathrm{64}}=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.......................... \\ $$

Question Number 140020 Answers: 0 Comments: 1

Question Number 140008 Answers: 1 Comments: 0

If in a number system 25×32=1163 find how many digits are there in the number system used.

$$\:{If}\:{in}\:{a}\:{number}\:{system} \\ $$$$\:\:\mathrm{25}×\mathrm{32}=\mathrm{1163} \\ $$$${find}\:{how}\:{many}\:{digits}\:{are}\:{there} \\ $$$${in}\:{the}\:{number}\:{system}\:{used}. \\ $$

Question Number 140007 Answers: 2 Comments: 0

lim_(x→0) (1+(3/x))^x =?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{1}+\frac{\mathrm{3}}{\mathrm{x}}\right)^{\mathrm{x}} =? \\ $$

Question Number 140002 Answers: 1 Comments: 0

Question Number 140000 Answers: 2 Comments: 2

lim_(x→0) (((1+x.2^x )/(1+x.3^x )))^(2/x^2 ) =?

$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}+\mathrm{x}.\mathrm{2}^{\mathrm{x}} }{\mathrm{1}+\mathrm{x}.\mathrm{3}^{\mathrm{x}} }\right)^{\frac{\mathrm{2}}{\mathrm{x}^{\mathrm{2}} }} =? \\ $$

Question Number 139998 Answers: 1 Comments: 1

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