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Question Number 135101 Answers: 1 Comments: 3

Question Number 135100 Answers: 0 Comments: 0

Question Number 135099 Answers: 2 Comments: 0

Question Number 135098 Answers: 0 Comments: 0

Question Number 135091 Answers: 0 Comments: 1

find (1)∫_C ZImZ^2 dz if C={∣Z∣=1:−π≤θ≤0} (2)∫_C (dz/(Z^4 +1)) if C=∣z−1+2i∣=(1/4) help me sir

$${find} \\ $$$$\left(\mathrm{1}\right)\int_{{C}} {ZImZ}^{\mathrm{2}} {dz}\:\:{if}\:{C}=\left\{\mid{Z}\mid=\mathrm{1}:−\pi\leqslant\theta\leqslant\mathrm{0}\right\} \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\int_{{C}} \frac{{dz}}{{Z}^{\mathrm{4}} +\mathrm{1}}\:\:\:{if}\:{C}=\mid{z}−\mathrm{1}+\mathrm{2}{i}\mid=\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$ \\ $$$${help}\:{me}\:{sir} \\ $$

Question Number 135090 Answers: 0 Comments: 0

Question Number 135065 Answers: 0 Comments: 2

cosec^2 68° +sec^2 56° −cot^2 34° −tan^2 22° =?

$$\mathrm{cosec}\:^{\mathrm{2}} \mathrm{68}°\:+\mathrm{sec}\:^{\mathrm{2}} \mathrm{56}°\:−\mathrm{cot}\:^{\mathrm{2}} \mathrm{34}°\:−\mathrm{tan}\:^{\mathrm{2}} \mathrm{22}°\:=? \\ $$

Question Number 135062 Answers: 1 Comments: 0

Let f(0) = a ; f(3)=0 and f ′(x)=e^x^4 what is the value ∫_0 ^( 3) x^2 f(x) dx ?

$$\mathrm{Let}\:\mathrm{f}\left(\mathrm{0}\right)\:=\:\mathrm{a}\:;\:\mathrm{f}\left(\mathrm{3}\right)=\mathrm{0}\:\mathrm{and}\:\mathrm{f}\:'\left(\mathrm{x}\right)=\mathrm{e}^{\mathrm{x}^{\mathrm{4}} } \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\int_{\mathrm{0}} ^{\:\mathrm{3}} \mathrm{x}^{\mathrm{2}} \:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:? \\ $$

Question Number 135061 Answers: 1 Comments: 0

How can I solve the differential equation (1+x^2)^2y′′+2x(1+x^2)y′+4y=0

$$ \\ $$How can I solve the differential equation (1+x^2)^2y′′+2x(1+x^2)y′+4y=0

Question Number 135060 Answers: 1 Comments: 0

Given that a > 3 and ax^2 + 7x - C=0 has real roots. What is the minimum value of Integer C?

$$ \\ $$Given that a > 3 and ax^2 + 7x - C=0 has real roots. What is the minimum value of Integer C?

Question Number 135034 Answers: 0 Comments: 0

...nice calculus if n≥2 and P_n =Π_(n=1) ^(n−1) sin(((kπ)/n)) find :: lim_(n→∞) ((nP_n )/2) ∫_(π/6) ^( (π/3)) ((cos(3x))/(sin^n (x)))dx

$$\:\:\:\:\:\:\:\:\:...{nice}\:\:\:{calculus}\:\: \\ $$$$\:\:\:\:{if}\:\:{n}\geqslant\mathrm{2}\:\:\:{and}\:\:\:{P}_{{n}} =\underset{{n}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\prod}}{sin}\left(\frac{{k}\pi}{{n}}\right) \\ $$$$\:\:\:\:\:{find}\:::\:{lim}_{{n}\rightarrow\infty} \frac{{nP}_{{n}} }{\mathrm{2}}\:\int_{\frac{\pi}{\mathrm{6}}} ^{\:\frac{\pi}{\mathrm{3}}} \frac{{cos}\left(\mathrm{3}{x}\right)}{{sin}^{{n}} \left({x}\right)}{dx} \\ $$

Question Number 135033 Answers: 0 Comments: 0

Question Number 135055 Answers: 1 Comments: 0

....dilogarithm integral.... calculate::: 𝛗=∫_0 ^( 1) li_2 (1−x^2 )dx=?

$$\:\:\:\:\:\:\:\:\:\:\:\:....{dilogarithm}\:\:\:{integral}.... \\ $$$$\:\:\:\:\:\:\:\:\:{calculate}::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} {li}_{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right){dx}=? \\ $$$$ \\ $$$$ \\ $$

Question Number 135054 Answers: 2 Comments: 3

Question Number 135024 Answers: 0 Comments: 7

Question Number 135019 Answers: 1 Comments: 0

Question Number 135004 Answers: 1 Comments: 6

the closest distance from the point on the curve y = x ^ 3-1 to the curve x = y ^2+ 4 is equal to

$$ \\ $$the closest distance from the point on the curve y = x ^ 3-1 to the curve x = y ^2+ 4 is equal to

Question Number 135000 Answers: 1 Comments: 0

Find the equation of the circle through the points of intersection of x^2+y^2−1=0,x^2+y^2−2x−4y+1=0 and touching the line x+2y=0?

$$ \\ $$Find the equation of the circle through the points of intersection of x^2+y^2−1=0,x^2+y^2−2x−4y+1=0 and touching the line x+2y=0?

Question Number 134998 Answers: 0 Comments: 0

Let I= ∫_(∣z∣=π) ((tan(z^− ))/(z−4)) dz J=∫_(∣z∣=π) ((cos(z^− ))/(z−4)) dz and K=∫_(∣z∣=π) ((cos(Re(z))cos(Im(z)))/(z−4))dz Show that I=J(√2)=−iπ Show that J=K

$$\:\:\:{Let}\:\:{I}=\:\int_{\mid{z}\mid=\pi} \frac{{tan}\left(\overset{−} {{z}}\right)}{{z}−\mathrm{4}}\:{dz}\:\: \\ $$$$\:{J}=\int_{\mid{z}\mid=\pi} \frac{{cos}\left(\overset{−} {{z}}\right)}{{z}−\mathrm{4}}\:{dz}\:\:\:{and}\:\:{K}=\int_{\mid{z}\mid=\pi} \frac{{cos}\left({Re}\left({z}\right)\right){cos}\left({Im}\left({z}\right)\right)}{{z}−\mathrm{4}}{dz} \\ $$$$\:{Show}\:{that}\:\:{I}={J}\sqrt{\mathrm{2}}=−{i}\pi \\ $$$$\:{Show}\:{that}\:\:{J}={K} \\ $$

Question Number 134993 Answers: 0 Comments: 0

Question Number 134989 Answers: 0 Comments: 0

Question Number 134986 Answers: 0 Comments: 0

Question Number 134987 Answers: 1 Comments: 0

Question Number 134984 Answers: 2 Comments: 0

(1^2 /2)+(((1+(1/2))^2 )/2^2 )+(((1+(1/2)+(1/3))^2 )/2^3 )+(((1+(1/2)+(1/3)+(1/4))^2 )/2^4 )+... Find in a closed form

$$\frac{\mathrm{1}^{\mathrm{2}} }{\mathrm{2}}+\frac{\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} }+\frac{\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}\right)^{\mathrm{2}} }{\mathrm{2}^{\mathrm{3}} }+\frac{\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{2}} }{\mathrm{2}^{\mathrm{4}} }+... \\ $$$$ \\ $$Find in a closed form

Question Number 134977 Answers: 1 Comments: 0

Question Number 134981 Answers: 1 Comments: 0

(a+1)(b+1)(c+1)=2abc a,b,c ε N

$$\left(\mathrm{a}+\mathrm{1}\right)\left(\boldsymbol{\mathrm{b}}+\mathrm{1}\right)\left(\boldsymbol{\mathrm{c}}+\mathrm{1}\right)=\mathrm{2}\boldsymbol{\mathrm{abc}}\: \\ $$$$\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}},\boldsymbol{\mathrm{c}}\:\varepsilon\:\mathrm{N} \\ $$

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