Recent content by ak123456

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    How to prove f(a) is integrable?

    Riemann integrability
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    How to prove f(a) is integrable?

    Homework Statement f(a)=a^2 on the interval [0,1],how to prove it by the definition of integral ,and to find \intf(a) on the interval [0,1] Homework Equations The Attempt at a Solution to prove by step functions ? set ai= (i/n)^(1/2) ??
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    Solving: Showing Sequence Converges to a Single Point

    still confusing
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    How can the convergence of a sequence be proven using the Squeeze Law method?

    but how can i apply Squeeze law.
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    How can the convergence of a sequence be proven using the Squeeze Law method?

    1. The problem statement, all variablproves and given/known data X0=1, Xn+1=1/4 (1+2/Xn) for n=0,1,2,3,4... prove that this sequence converges ,and find the limit Homework Equations The Attempt at a Solution I though that Squeeze law might be used ,and let L=1/4(1+2/L) L=0.8437...
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    What is the Proof of sup(A)+1 as the Least Upper Bound for B=A+1?

    i see ,thx
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    Solving: Showing Sequence Converges to a Single Point

    1. Homework Statement [/b] Let Jn : n \inN be a sequence of intervals Jn=\left[an,bn\right] such that J1\supsetJ2\supset...\supsetJn\supsetJn+1\supset... suppose also that the sequence xn=an-bn converges to 0 as n tends to infinite.Show that there is exactly one point a such that a\inJn for...
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    What is the Proof of sup(A)+1 as the Least Upper Bound for B=A+1?

    Homework Statement Let A \inR be a non-empty,bounded set .Define B=A+1=\left\{a+1:a\inA\right\} Prove that sup(B) =sup(A)+1 Homework Equations The Attempt at a Solution let a\inA b\inB s\inR because B=A+1=\left\{a+1:a\inA\right\} so b=a+1 \forallb\inB s>= b \rightarrow s>=a+1 , s>=a so...
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    Normal Distribution with Non-Standard Mean and Variance: Solving for P(X>1)

    Homework Statement how to do with the normal distribution if the mean is not 0 variance is not 1. for example p(x>1) if x-N(2,3) ? Homework Equations The Attempt at a Solution
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    Simplifying the Poisson Distribution Formula: Integration and Infinite Series

    any help?
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    Simplifying the Poisson Distribution Formula: Integration and Infinite Series

    b]1. Homework Statement [/b] prove that \sum( (e^(-u)) (u(^(x)) )/x! (from x=o to n ) = \int ( (e^(-y))(y^n) )dy/n! (from u to infinite ) Homework Equations The Attempt at a Solution i know that the left is Poisson distribution formula but how to do with the 'sum' ? and...
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    Linear transformation and polynomial function

    Homework Statement from calculus we know that ,for any polynomial function f : R-R of degree <= n,the fuction of I(f) :R-R ,s----\intf(u) du is a polynomial function of degree <=n+1 show that the map I: Pn--Pn+1 , f--I(f) is an injective linear transformation, determine a basis of the image...
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    Is this an isomorphism between vector spaces

    Homework Statement a belongs to R show that the map L: R^n------R^n>0 (R^n>0 denote the n-fold cartesian product of R>0 with itself) (a1) (...) ---------- (an) (e^a1) (...) (e^an) is a isomorphism between the vector space R^n and the vector space R^n>0 Homework Equations...
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    Satisfies Cauchy-Riemann equations but not differentiable

    _z is x-iy
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    Satisfies Cauchy-Riemann equations but not differentiable

    Homework Statement Let f denote the function defined by f(z)= _z^2 /z if z is not 0 0 if z=0 show that f satisfies the Cauchy-Riemann equations at z=0 but that f is not differentiable there Homework Equations The Attempt at a Solution it is easily to show the...