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UC Davis #10: count prove Σi = n(n+1)/2 where i=1 to n
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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(x)) dx
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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx
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logic Idempotent law show x=xVx
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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Penn. State U: Suppose the p.m.f of discrete random variable X is ...
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logic: tautology (¬p→q)∧(¬p→¬q) →p
Review: Linear form, Quadratic form & Bilinear form
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diff eq: Solve dy/dx = (2y4x^4)/(xy^3) ❌separable to ✅separable
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Review: Multiplying each obs. by a CONSTANT results in new variance =
prob stat: Compute Var(X) when X represents the outcome when we roll a fair die.
Calculus: If u=f(x+cy)+g(x-cy) then uxx / uyy ?
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The pth, qth, & rth terms of an AP are x,y,z respectively.
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#17 2020 MIT Integration Bee Quali Exam:
example: Mean, Median & Mode
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2 ways: trig integral ∫1/(2+cos^2(x)) dx
STPM Math T Sem. 2: Ex 11.2 Given that f(x)=tan(x), show that ...
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2nd/3 ways: How many chords can be drawn through 21 points on a circle?
UC Davis#2: 2nd way integral ∫(2x+3)/(x^2-9) dx [integration by partial fraction]