Find condition on $t$ such that $ |xi(t) |leq 1$ Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Closed and exact.Integral in spherical coordinates, $Omega$ is the unit sphere, of $iiint_Omega 1/(2+z)^2dx dy dz$Bound for this integralFinding a value R that maximizes the flux a vector field over half a sphere of radius RProving the inequality $2^-1+frac1nleft(x+1right)leqleft(x^n+1right)^frac1n$ for $ninmathbbN $ and $x>0$Find the area of a “petal” of a polar curve using Green's TheoremMaxima of almost quadratic function.How to use error propagation in calculusInequality involving Mobius transformationEvaluating $oint_C vecF cdot dvecr$
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Find condition on $t$ such that $ |xi(t) |leq 1$
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Closed and exact.Integral in spherical coordinates, $Omega$ is the unit sphere, of $iiint_Omega 1/(2+z)^2dx dy dz$Bound for this integralFinding a value R that maximizes the flux a vector field over half a sphere of radius RProving the inequality $2^-1+frac1nleft(x+1right)leqleft(x^n+1right)^frac1n$ for $ninmathbbN $ and $x>0$Find the area of a “petal” of a polar curve using Green's TheoremMaxima of almost quadratic function.How to use error propagation in calculusInequality involving Mobius transformationEvaluating $oint_C vecF cdot dvecr$
$begingroup$
Let $a, b in mathbb C$, $x,theta in mathbb R$, $x>0$
I'm looking for a (strict, if possible) condition on $t > 0$ such that the number $|xi(t)| = |1 - frac2atx^2sin^2(fractheta2)+bt|$ will be no greater than $1$ for all $theta$.
What I tried:
Writing $a = a_R + ia_I, b = b_R + ib_I$ we thus have
$|xi(t)|^2 = |1 - frac2(a_R + ia_I)tx^2sin^2(fractheta2)+(b_R + ib_I)t|^2 = |(1-frac2a_Rtx^2sin^2(fractheta2)+b_Rt)+i(-frac2a_Itx^2sin^2(fractheta2)+b_It)|^2=(1-frac2a_Rtx^2sin^2(fractheta2)+b_Rt)^2+(-frac2a_Itx^2sin^2(fractheta2)+b_It)^2 = dots$
I got to a very ugly term with $t$ and $t^2$ and there's no obvious way to proceed.
calculus inequality complex-numbers
asked Apr 8 at 20:03
Rick JokerRick Joker
283214
$endgroup$
add a comment |
$begingroup$
Let $a, b in mathbb C$, $x,theta in mathbb R$, $x>0$
I'm looking for a (strict, if possible) condition on $t > 0$ such that the number $|xi(t)| = |1 - frac2atx^2sin^2(fractheta2)+bt|$ will be no greater than $1$ for all $theta$.
What I tried:
Writing $a = a_R + ia_I, b = b_R + ib_I$ we thus have
$|xi(t)|^2 = |1 - frac2(a_R + ia_I)tx^2sin^2(fractheta2)+(b_R + ib_I)t|^2 = |(1-frac2a_Rtx^2sin^2(fractheta2)+b_Rt)+i(-frac2a_Itx^2sin^2(fractheta2)+b_It)|^2=(1-frac2a_Rtx^2sin^2(fractheta2)+b_Rt)^2+(-frac2a_Itx^2sin^2(fractheta2)+b_It)^2 = dots$
I got to a very ugly term with $t$ and $t^2$ and there's no obvious way to proceed.
calculus inequality complex-numbers
asked Apr 8 at 20:03
Rick JokerRick Joker
283214
$endgroup$
add a comment |
$begingroup$
Let $a, b in mathbb C$, $x,theta in mathbb R$, $x>0$
I'm looking for a (strict, if possible) condition on $t > 0$ such that the number $|xi(t)| = |1 - frac2atx^2sin^2(fractheta2)+bt|$ will be no greater than $1$ for all $theta$.
What I tried:
Writing $a = a_R + ia_I, b = b_R + ib_I$ we thus have
$|xi(t)|^2 = |1 - frac2(a_R + ia_I)tx^2sin^2(fractheta2)+(b_R + ib_I)t|^2 = |(1-frac2a_Rtx^2sin^2(fractheta2)+b_Rt)+i(-frac2a_Itx^2sin^2(fractheta2)+b_It)|^2=(1-frac2a_Rtx^2sin^2(fractheta2)+b_Rt)^2+(-frac2a_Itx^2sin^2(fractheta2)+b_It)^2 = dots$
I got to a very ugly term with $t$ and $t^2$ and there's no obvious way to proceed.
calculus inequality complex-numbers
asked Apr 8 at 20:03
Rick JokerRick Joker
283214
$endgroup$
Let $a, b in mathbb C$, $x,theta in mathbb R$, $x>0$
I'm looking for a (strict, if possible) condition on $t > 0$ such that the number $|xi(t)| = |1 - frac2atx^2sin^2(fractheta2)+bt|$ will be no greater than $1$ for all $theta$.
What I tried:
Writing $a = a_R + ia_I, b = b_R + ib_I$ we thus have
$|xi(t)|^2 = |1 - frac2(a_R + ia_I)tx^2sin^2(fractheta2)+(b_R + ib_I)t|^2 = |(1-frac2a_Rtx^2sin^2(fractheta2)+b_Rt)+i(-frac2a_Itx^2sin^2(fractheta2)+b_It)|^2=(1-frac2a_Rtx^2sin^2(fractheta2)+b_Rt)^2+(-frac2a_Itx^2sin^2(fractheta2)+b_It)^2 = dots$
I got to a very ugly term with $t$ and $t^2$ and there's no obvious way to proceed.
calculus inequality complex-numbers
calculus inequality complex-numbers
asked Apr 8 at 20:03
Rick JokerRick Joker
283214
asked Apr 8 at 20:03
Rick JokerRick Joker
283214
asked Apr 8 at 20:03
Rick JokerRick Joker
283214
asked Apr 8 at 20:03
Rick JokerRick Joker
283214
asked Apr 8 at 20:03
Rick JokerRick Joker
283214
283214
add a comment |
add a comment |
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