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I am math lecturer from Lithuania and teach math first and second year university students. I like helping people understand mathematics and find activity of solving problems here interesting and useful. Smile and the world will smile you back! :) ================================ Some useful symbols t³ x² ±√ ∫ ° ⋀ ⋁ ¬ π ¶ ° ¹ x² ³ ⁴ ª ⁿ ₁ ₂ ← → ⇒ ∀ ∃ ∇ ∂ ∑ ∞ ≅ ≈ ≠ ≤ ≥ ½ ⅓ ⅔ ¼ ¾ ⅛ ⅜ ⅝ ⅞ α β γ δ ε ζ η θ λ μ ξ ρ Σ σ φ ψ ω Subscripts---- N₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₀ ₊ ₋ ₌ ₍ ₎ Superscripts----N º ¹ ² ³ ⁰ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁼ ⁽ ⁾ ⁿ Fractions-----¼ ½ ⅓ ⅔ ¾ ⅓ ⅛ ⅜ ⅝ ⅞ ⅓ ⅔ ⅕ ⅖ ⅗ ⅘ ⅙ ⅚ ⅛ ⅜ ⅝ ⅞ http://tlt.its.psu.edu/suggestions/international/bylanguage/mathchart.html#common

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  • <<Integral depending on parameter >>?

    Evaluate integral J(x,p) = [0, 1] ∫ [atan(p*x)] /[x*√(1-x²)] dx using differentiation by parameter.

    3 AnswersMathematics1 decade ago

  • *****Loop integral 2009*****?

    Evaluate loop integral L ∫dz/(2009 + z^2009) , when

    1) L: |z| = 1;

    2) L: | 2z - √7| + | 2z + √7| = 8.

    2 AnswersMathematics1 decade ago

  • Tiny integral with huuuuuuge integration?

    Integrate ∫ (9 + 4/√x )^3/2 dx.

    I have two solutions. So I am more interested in the shortest solution :)

    What method do you use to integrate it and what is the final answer?

    4 AnswersMathematics1 decade ago

  • Series: Leibniz’s test – sufficient but not necessary!?

    Let {a_n} be some sequence, a_n >=0.

    Leibniz’s test is used to prove that alternating series

    Σa_n*(-1)^n is convergent.

    It states that: if lim (a_n) =0 as n-> ∞ and the sequence {a_n}

    is monotone decreasing then the alternating series Σa_n*(-1)^n converges.

    Conditions of the Leibniz’s test are sufficient but not necessary.

    So, construct such alternating series which do not satisfy

    conditions of the Leibniz’s test however converges and

    general term of which is a_n = f(n), where

    1) f(x) continuous;

    2) f(x) discontinuous,

    x є R, n є N.

    1 AnswerMathematics1 decade ago

  • Curious…Combinatorics?

    I didn’t succeed in solving this problem. Now just curious :)

    This story is told in one Arabian tale.

    12 men (cutthroats) sat in a circle around the fire. Each of them bloody hated his neighbours from both sides. They needed 5 men to hide a treasure. In how many ways it is possible to make a group of 5 cutthroats for hiding treasure that they wouldn’t kill each other?

    The answer given – 36.

    1 AnswerMathematics1 decade ago