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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.

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

Question Number 56146 Answers: 1 Comments: 1

Given complex number z_1 , z_2 , and z_3 satiesfied z_1 +z_2 +z_3 =0 and ∣z_1 ∣=∣z_2 ∣=∣z_3 ∣=1. Prove that z_1 ^2 +z_2 ^2 +z_3 ^2 =0

$$\mathrm{Given}\:\mathrm{complex}\:\mathrm{number} \\ $$$${z}_{\mathrm{1}} ,\:{z}_{\mathrm{2}} ,\:\mathrm{and}\:{z}_{\mathrm{3}} \:\mathrm{satiesfied}\:{z}_{\mathrm{1}} +{z}_{\mathrm{2}} +{z}_{\mathrm{3}} =\mathrm{0} \\ $$$$\mathrm{and}\:\mid{z}_{\mathrm{1}} \mid=\mid{z}_{\mathrm{2}} \mid=\mid{z}_{\mathrm{3}} \mid=\mathrm{1}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$${z}_{\mathrm{1}} ^{\mathrm{2}} +{z}_{\mathrm{2}} ^{\mathrm{2}} +{z}_{\mathrm{3}} ^{\mathrm{2}} =\mathrm{0} \\ $$

Question Number 56145 Answers: 1 Comments: 0

find residu of function f(z)=(e^(1/z) /(z^2 +1)) in z=0

$$\mathrm{find}\:\mathrm{residu}\:\mathrm{of}\:\mathrm{function} \\ $$$${f}\left({z}\right)=\frac{{e}^{\frac{\mathrm{1}}{{z}}} }{{z}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{in}\:{z}=\mathrm{0} \\ $$

Question Number 56144 Answers: 1 Comments: 0

calculate (i−1)^(49) (cos (π/(40))+i sin (π/(40)))^(10)

$$\mathrm{calculate}\:\left({i}−\mathrm{1}\right)^{\mathrm{49}} \left(\mathrm{cos}\:\frac{\pi}{\mathrm{40}}+{i}\:\mathrm{sin}\:\frac{\pi}{\mathrm{40}}\right)^{\mathrm{10}} \\ $$

Question Number 72830 Answers: 2 Comments: 0

The value of x satisfying the inequalities (((2x−1)(x−1)^4 (x−2)^4 )/((x−2)(x−4)^4 ))≤ 0

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:{x}\:\mathrm{satisfying}\:\mathrm{the}\: \\ $$$$\mathrm{inequalities}\:\frac{\left(\mathrm{2}{x}−\mathrm{1}\right)\left({x}−\mathrm{1}\right)^{\mathrm{4}} \left({x}−\mathrm{2}\right)^{\mathrm{4}} }{\left({x}−\mathrm{2}\right)\left({x}−\mathrm{4}\right)^{\mathrm{4}} }\leqslant\:\mathrm{0} \\ $$

Question Number 72829 Answers: 0 Comments: 0

Σ_(k=m) ^n ^k C_r equals

$$\underset{{k}={m}} {\overset{{n}} {\sum}}\:^{{k}} {C}_{{r}} \:\mathrm{equals} \\ $$

Question Number 56142 Answers: 0 Comments: 0

If n is even and rth term has the greatest coefficient in the binomial expansion of (1+x)^n , then

$$\mathrm{If}\:{n}\:\mathrm{is}\:\mathrm{even}\:\mathrm{and}\:{r}\mathrm{th}\:\mathrm{term}\:\mathrm{has}\:\mathrm{the}\:\mathrm{greatest} \\ $$$$\mathrm{coefficient}\:\mathrm{in}\:\mathrm{the}\:\mathrm{binomial}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left(\mathrm{1}+{x}\right)^{{n}} ,\:\mathrm{then} \\ $$

Question Number 56141 Answers: 1 Comments: 0

If (1+x)^n =C_0 +C_1 x+C_2 x^2 +...+C_n x^n , then for n odd, C_0 ^2 −C_1 ^2 +C_2 ^2 −C_3 ^2 +...+(−1)^n C_n ^2 is equal to

$$\mathrm{If}\:\left(\mathrm{1}+{x}\right)^{{n}} ={C}_{\mathrm{0}} +{C}_{\mathrm{1}} {x}+{C}_{\mathrm{2}} {x}^{\mathrm{2}} +...+{C}_{{n}} {x}^{{n}} ,\:\mathrm{then} \\ $$$$\mathrm{for}\:{n}\:\mathrm{odd},\:{C}_{\mathrm{0}} \:^{\mathrm{2}} −{C}_{\mathrm{1}} \:^{\mathrm{2}} +{C}_{\mathrm{2}} \:^{\mathrm{2}} −{C}_{\mathrm{3}} \:^{\mathrm{2}} +...+\left(−\mathrm{1}\right)^{{n}} {C}_{{n}} \:^{\mathrm{2}} \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 56140 Answers: 1 Comments: 0

The value of 2 C_0 +(2^2 /2)C_1 +(2^3 /3)C_2 +(2^4 /4)C_3 +...+(2^(11) /(11))C_(10) is

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\:\: \\ $$$$\mathrm{2}\:{C}_{\mathrm{0}} +\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{2}}{C}_{\mathrm{1}} +\frac{\mathrm{2}^{\mathrm{3}} }{\mathrm{3}}{C}_{\mathrm{2}} +\frac{\mathrm{2}^{\mathrm{4}} }{\mathrm{4}}{C}_{\mathrm{3}} +...+\frac{\mathrm{2}^{\mathrm{11}} }{\mathrm{11}}{C}_{\mathrm{10}} \:\:\mathrm{is} \\ $$

Question Number 56139 Answers: 1 Comments: 0

If x+y=1, then Σ_(r=0) ^n r^2 ^n C_r x^r y^(n−r) equals

$$\mathrm{If}\:{x}+{y}=\mathrm{1},\:\mathrm{then}\:\:\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\:{r}^{\mathrm{2}} \:\:^{{n}} {C}_{{r}} \:{x}^{{r}} \:{y}^{{n}−{r}} \:\mathrm{equals} \\ $$

Question Number 56138 Answers: 1 Comments: 2

The pisitive value of a so that the coefficient of x^5 and x^(15) are equal in the expansion of (x^2 + (a/x^3 ))^(10)

$$\mathrm{The}\:\mathrm{pisitive}\:\mathrm{value}\:\mathrm{of}\:\:{a}\:\mathrm{so}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{coefficient}\:\mathrm{of}\:{x}^{\mathrm{5}} \:\mathrm{and}\:{x}^{\mathrm{15}} \:\mathrm{are}\:\mathrm{equal}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left({x}^{\mathrm{2}} +\:\frac{{a}}{{x}^{\mathrm{3}} }\right)^{\mathrm{10}} \\ $$

Question Number 56137 Answers: 1 Comments: 1

If (1+2x+x^2 )^n = Σ_(r=0) ^(2n) a_r x^r , then a_r =

$$\mathrm{If}\:\left(\mathrm{1}+\mathrm{2}{x}+{x}^{\mathrm{2}} \right)^{{n}} \:=\:\underset{{r}=\mathrm{0}} {\overset{\mathrm{2}{n}} {\sum}}\:{a}_{{r}} \:{x}^{{r}} ,\:\mathrm{then}\:{a}_{{r}} = \\ $$

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