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Question Number 56280 Answers: 2 Comments: 2

Evaluate : 1) ((∫_0 ^( 1_ ) (1−(1−x^2 )^(100) )^(201) .xdx)/(∫_0 ^( 1) (1−(1−x^2 )^(100) )^(202) .xdx)) = ? 2) ((∫_0 ^( 1) (1−x^(200) )^(201) dx)/(∫_0 ^( 1) (1−x^(200) )^(202) dx)) = ?

$${Evaluate}\:: \\ $$$$\left.\mathrm{1}\right)\:\frac{\int_{\mathrm{0}} ^{\:\mathrm{1}_{} } \left(\mathrm{1}−\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{100}} \right)^{\mathrm{201}} \:.{xdx}}{\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\mathrm{1}−\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{100}} \right)^{\mathrm{202}} .{xdx}}\:=\:? \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\:\frac{\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{200}} \right)^{\mathrm{201}} {dx}}{\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{200}} \right)^{\mathrm{202}} {dx}}\:=\:? \\ $$

Question Number 56264 Answers: 0 Comments: 3

(x_C −h)^2 +3((s/2)−x_C )^2 = a^2 (x_A −h)^2 +3((s/2)+x_A )^2 = c^2 (x_C −x_A )^2 = b^2 /4 .

$$\left({x}_{{C}} −{h}\right)^{\mathrm{2}} +\mathrm{3}\left(\frac{{s}}{\mathrm{2}}−{x}_{{C}} \right)^{\mathrm{2}} \:=\:{a}^{\mathrm{2}} \\ $$$$\:\left({x}_{{A}} −{h}\right)^{\mathrm{2}} +\mathrm{3}\left(\frac{{s}}{\mathrm{2}}+{x}_{{A}} \right)^{\mathrm{2}} =\:{c}^{\mathrm{2}} \\ $$$$\:\:\left({x}_{{C}} −{x}_{{A}} \right)^{\mathrm{2}} \:=\:{b}^{\mathrm{2}} /\mathrm{4}\:. \\ $$

Question Number 56245 Answers: 2 Comments: 1

Question Number 56244 Answers: 0 Comments: 7

Is ∞ a complex number. If not so what is It.

$${Is}\:\infty\:{a}\:{complex}\:{number}. \\ $$$${If}\:{not}\:{so}\:{what}\:{is}\:{It}. \\ $$

Question Number 56243 Answers: 1 Comments: 0

6/2×5 which one correct 6/2×5 6/2×5 =3×5 =6/10 =15 =0.6

$$\mathrm{6}/\mathrm{2}×\mathrm{5} \\ $$$$\:{which}\:{one}\:{correct} \\ $$$$\mathrm{6}/\mathrm{2}×\mathrm{5}\:\:\:\:\:\:\:\:\:\:\:\mathrm{6}/\mathrm{2}×\mathrm{5} \\ $$$$=\mathrm{3}×\mathrm{5}\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{6}/\mathrm{10} \\ $$$$=\mathrm{15}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{0}.\mathrm{6} \\ $$

Question Number 56229 Answers: 2 Comments: 4

How can you prove (not geometrically) the following? Σ_(k = 0) ^n k = (( n ( n + 1 ) )/2)

$$\mathrm{How}\:\mathrm{can}\:\mathrm{you}\:\mathrm{prove}\:\left(\mathrm{not}\:\mathrm{geometrically}\right) \\ $$$$\mathrm{the}\:\mathrm{following}? \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\underset{{k}\:=\:\mathrm{0}} {\overset{{n}} {\sum}}{k}\:\:=\:\:\frac{\:{n}\:\left(\:{n}\:+\:\mathrm{1}\:\right)\:}{\mathrm{2}} \\ $$$$ \\ $$

Question Number 56215 Answers: 4 Comments: 2

(√(x/(x−1)))+(√((x−1)/x))=2 find x

$$\sqrt{\frac{{x}}{{x}−\mathrm{1}}}+\sqrt{\frac{{x}−\mathrm{1}}{{x}}}=\mathrm{2} \\ $$$$ \\ $$$${find}\:{x} \\ $$

Question Number 56214 Answers: 3 Comments: 0

x^x =4 find x

$${x}^{{x}} =\mathrm{4} \\ $$$$ \\ $$$${find}\:{x} \\ $$

Question Number 56213 Answers: 1 Comments: 1

xsin x=5 find x

$${x}\mathrm{sin}\:{x}=\mathrm{5} \\ $$$$ \\ $$$${find}\:{x} \\ $$

Question Number 56212 Answers: 1 Comments: 0

In how many ways can 4 boys and 3 girls stand in a straight line a. if there are no restrictions b. if the boys stand next to each other

$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{4}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{3}\:\mathrm{girls} \\ $$$$\mathrm{stand}\:\mathrm{in}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line} \\ $$$$\mathrm{a}.\:\mathrm{if}\:\mathrm{there}\:\mathrm{are}\:\mathrm{no}\:\mathrm{restrictions} \\ $$$$\mathrm{b}.\:\mathrm{if}\:\mathrm{the}\:\mathrm{boys}\:\mathrm{stand}\:\mathrm{next}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other} \\ $$

Question Number 56205 Answers: 1 Comments: 0

find (or prove it can′t exist) a f:R→R diferentiable such that ∫_(a−δ) ^(a+δ) f(x)dx=0,∀a∈R,δ>0 (df/dx)=0,∀x∈R

$$\mathrm{find}\:\left(\mathrm{or}\:\mathrm{prove}\:\mathrm{it}\:\mathrm{can}'\mathrm{t}\:\mathrm{exist}\right)\:\mathrm{a}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{diferentiable} \\ $$$$\mathrm{such}\:\mathrm{that} \\ $$$$\underset{{a}−\delta} {\overset{{a}+\delta} {\int}}{f}\left({x}\right){dx}=\mathrm{0},\forall{a}\in\mathbb{R},\delta>\mathrm{0} \\ $$$$\frac{{df}}{{dx}}=\mathrm{0},\forall{x}\in\mathbb{R} \\ $$

Question Number 56203 Answers: 0 Comments: 0

Question Number 56202 Answers: 1 Comments: 0

lim_(x→0) ((x^2 tan^(−1) (x) − 3 ∫_0 ^x sin (t^2 ) dt)/x^5 ) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\:\frac{{x}^{\mathrm{2}} \:\mathrm{tan}^{−\mathrm{1}} \left({x}\right)\:−\:\mathrm{3}\:\underset{\mathrm{0}} {\int}\:\overset{{x}} {\:}\:\mathrm{sin}\:\left({t}^{\mathrm{2}} \right)\:{dt}}{{x}^{\mathrm{5}} }\:\:=\:\:? \\ $$

Question Number 56200 Answers: 0 Comments: 5

Question Number 56192 Answers: 1 Comments: 0

find z_1 ,z_2 ∈C (1/(z_1 +z_2 ))=(1/z_1 )+(1/z_2 )

$$\mathrm{find}\:{z}_{\mathrm{1}} ,{z}_{\mathrm{2}} \in\mathbb{C} \\ $$$$\frac{\mathrm{1}}{{z}_{\mathrm{1}} +{z}_{\mathrm{2}} }=\frac{\mathrm{1}}{{z}_{\mathrm{1}} }+\frac{\mathrm{1}}{{z}_{\mathrm{2}} } \\ $$

Question Number 56190 Answers: 0 Comments: 0

There was a post some time back for failed import. Can u please resend the email? Email address to be used is info@tinkutara.com Thanks

$$\mathrm{There}\:\mathrm{was}\:\mathrm{a}\:\mathrm{post}\:\mathrm{some}\:\mathrm{time}\:\mathrm{back} \\ $$$$\mathrm{for}\:\mathrm{failed}\:\mathrm{import}.\:\mathrm{Can}\:\mathrm{u}\:\mathrm{please} \\ $$$$\mathrm{resend}\:\mathrm{the}\:\mathrm{email}?\:\mathrm{Email}\:\mathrm{address} \\ $$$$\mathrm{to}\:\mathrm{be}\:\mathrm{used}\:\mathrm{is}\:\mathrm{info}@\mathrm{tinkutara}.\mathrm{com} \\ $$$$\mathrm{Thanks} \\ $$

Question Number 56189 Answers: 0 Comments: 2

let u_n =∫_(−∞) ^∞ ((sin(nx^2 ))/(x^2 +x +n)) dx 1) calculate u_n 2) find lim_(n→+∞) u_n 3) study the serie Σ u_n

$${let}\:{u}_{{n}} =\int_{−\infty} ^{\infty} \:\:\:\frac{{sin}\left({nx}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} +{x}\:+{n}}\:{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:{u}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} {u}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{study}\:{the}\:{serie}\:\Sigma\:{u}_{{n}} \\ $$

Question Number 56188 Answers: 1 Comments: 0

find the value of ∫_0 ^∞ (((1+x)^(−(1/4)) −(1+x)^(−(3/4)) )/x) dx

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\left(\mathrm{1}+{x}\right)^{−\frac{\mathrm{1}}{\mathrm{4}}} −\left(\mathrm{1}+{x}\right)^{−\frac{\mathrm{3}}{\mathrm{4}}} }{{x}}\:{dx} \\ $$

Question Number 56187 Answers: 0 Comments: 0

study the convergence of ∫_0 ^∞ (((1+x)^α −(1+x)^β )/x) dx .

$${study}\:{the}\:{convergence}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\left(\mathrm{1}+{x}\right)^{\alpha} −\left(\mathrm{1}+{x}\right)^{\beta} }{{x}}\:{dx}\:\:. \\ $$

Question Number 56186 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((arctan(ix))/(2+x^2 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({ix}\right)}{\mathrm{2}+{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 56183 Answers: 1 Comments: 0

find all a,b∈R such that (1/(a+bi))=(1/a)+(i/b)

$$\mathrm{find}\:\mathrm{all}\:{a},{b}\in\mathbb{R}\:\mathrm{such}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{{a}+{bi}}=\frac{\mathrm{1}}{{a}}+\frac{{i}}{{b}} \\ $$

Question Number 56179 Answers: 1 Comments: 1

draw the graph of f(x)=(√(1−x^2 )) for 0≤x≤1

$$\mathrm{draw}\:\mathrm{the}\:\mathrm{graph}\:\mathrm{of} \\ $$$$\mathrm{f}\left({x}\right)=\sqrt{\mathrm{1}−{x}^{\mathrm{2}} } \\ $$$$\mathrm{for}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1} \\ $$

Question Number 56169 Answers: 1 Comments: 0

∫^1 _(−∞) (a+bi)^x dx=?

$$\underset{−\infty} {\int}^{\mathrm{1}} \left({a}+{b}\mathrm{i}\right)^{{x}} {dx}=? \\ $$

Question Number 56166 Answers: 0 Comments: 1

Question Number 56165 Answers: 1 Comments: 0

Question Number 56147 Answers: 1 Comments: 6

if ∫_( 1) ^( 2) f(x) dx = (√( 2 )), then ∫_( 1) ^( 4) (1/((√( x )) )) f(x) dx is ?? please help me Sir. I′ve been trying this for 2 days and getting stuck.

$$\mathrm{if}\:\underset{\:\:\mathrm{1}} {\overset{\:\:\mathrm{2}} {\int}}\:{f}\left({x}\right)\:{dx}\:=\:\sqrt{\:\mathrm{2}\:},\:\mathrm{then}\:\underset{\:\:\mathrm{1}} {\overset{\:\:\mathrm{4}} {\int}}\:\frac{\mathrm{1}}{\sqrt{\:{x}\:}\:}\:{f}\left({x}\right)\:{dx} \\ $$$$\:\mathrm{is}\:?? \\ $$$$\:\:\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{Sir}.\:\mathrm{I}'\mathrm{ve}\:\mathrm{been}\:\mathrm{trying} \\ $$$$\:\:\mathrm{this}\:\mathrm{for}\:\mathrm{2}\:\mathrm{days}\:\mathrm{and}\:\mathrm{getting}\:\mathrm{stuck}. \\ $$$$ \\ $$$$ \\ $$

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