COMMON MISTAKE: (1) logb(m) logb(n) ≠ logb(m+n)

exp integral e^2x/(1+e^x) dx

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Penn. State U: Suppose the p.m.f of discrete random variable X is ...

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prob stat In a sample of n= 6 scores, 5 of the scores are each above the mean by one point.

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expon directive a^f(x)

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Prove Σ1/((k-1)(k+1))=(3n^2-n-2)/(4n(n+1)) where k=2 to n ∀n ≥ 2

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2 ways: derivative a^f(g(x))

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sq root derivative √x [Good to know the result]

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Median [special weighted mean]

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5 ways: integral ∫a^(px+q) dx

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2 ways: trig Show tan(2x)=2/(cot(x)-tan(x))

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2nd way: ∫cos(x)/√(sin^2(x)+4sin(x)+3) dx

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1st/2ways: r-Permutations

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Lamar U 2nd way: evaluate integral ∫√(1+2ln(7x))/2 +10x^3/(x^4 +9) dx

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prob stat: Compute Var(X) when X represents the outcome when we roll a fair die.

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sum Find 1/1.4 + 1/4.7 +1/7.10+... +1/((3n-2)(3n+1))

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2nd way: trig integral ∫1/(1+sec(x)) dx

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2nd way: derivative y=e^x sin(x) cos^3(x)

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Evaluate these 7 integrals ...

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2 ways: 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫3x/((x-2)(x+1)) dx

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8Screen Recording 2023-12-07 at 1.55.57 AM

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