Recent content by a1010711

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    Approximating integral using riemann sums

    hi, I just thought I should point out that your upper riemann sum is less than your lower riemann sum. I'm sure you're well aware that for any parition P, we have that Spf >= spf. I suggest redrawing your graph making sure that you have chosen the appropriate height/width for the...
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    Group theory, is my solution correct?

    Homework Statement if H is a normal subgroup of G and has index n, show that g^n is in H for all g in G. The Attempt at a Solution Take H a normal subgroup of a group G. Take g in G. Consider gH in the quotient group G/H. Because |G/H| = [G:H] = n, (gH)^n = eH. But g^nH =...
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    Changing the order of integration

    Homework Statement Change the order of integration in the following double integral integral from o to a, integral from 0 to sqrt(2ay-y^2) f(x y) dx dy so i can see its a semi circle with center at (0,a) x= sqrt(2ay-y^2) can be expanded by squaring both sides. then completing...
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    Is L(x) Continuously Differentiable and Does L(xy) = L(x) + L(y)?

    Homework Statement let L(x)= integral from 1 to x: 1/t dt. Show that L:]0,infinity[--->R is continuously differentiable. show that L(xy)=L(x)+L(y) for all x,y in ]0,infinity[. hint: let L1(x)=L(xy) and compute L'1(x) you don't have to solve it for me, just lead me in the right...
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    Does the following integral converge

    Homework Statement the integral from 0 to 1 given: 1 / [ (x^1/3)(x^2+2x)^1/2 ] dx please explain,, thank you! The Attempt at a Solution At 0 the integrand behaves as 1/x^1/3*x^1/2 = 1/x^1/6 which is convergent as the exponent is <1
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    Prove that if f and g are integrable on [a, b], then so is fg

    The Attempt at a Solution It suffices to show that f^2 is integrable, since fg= [(f+g)^2-(f-g)^2]/4 The function x --> x^2 is uniformly continuous on the range of f, im not sure how to turn this into a formal proof, I am lost Riemann integration
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    Setting up triple integral in cylindrical coords (looking to check my answer)

    Homework Statement set up an integral in cylindrical coords to compute the volume of the solid S bounded by the sphere x^2+y^2+z^2=12 and the cone 3z^2=x^2+y^2 where z>=0 The Attempt at a Solution i will post my answer here. please let 'I' stand for integral: i get, I[0,2pi]...
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    Changing the order of integration

    Homework Statement change the order of integration in the follwing double integral: intgral [0,a] integral [0,sqrt(2ay-y^2)] f(x,y) dx dy if x= sqrt(2ay-y^2),, do i solve for y or something,,ive used the computer to graph it but that didnt help me.