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Pascal's triangle rCk [examples]

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logic: tautology (¬p→q)∧(¬p→¬q) →p
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logic: tautology (¬p→q)∧(¬p→¬q) →p

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx
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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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1st/2ways: logic Import-Export
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1st/2ways: logic Import-Export

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3rd/10parts: Exclusive disjunction
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3rd/10parts: Exclusive disjunction

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prob & stat: Show ...
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prob & stat: Show ...

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1st/2ways: permutation Show P(n,2)+P(n,1)=n^2
4:37

1st/2ways: permutation Show P(n,2)+P(n,1)=n^2

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3 ways: sum Show 1+3+5+...nth term = n^2
5:23

3 ways: sum Show 1+3+5+...nth term = n^2

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2nd way: trig integral ∫1/(cos(x)(1+cos(x)) dx
2:43

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

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2 ways: trig show tan(2x)=2tan(x)/1-tan^2(x))
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2 ways: trig show tan(2x)=2tan(x)/1-tan^2(x))

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Alternate way: Evaluate exp integral ∫1/√(1-e^(2x)) dx
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Alternate way: Evaluate exp integral ∫1/√(1-e^(2x)) dx

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4 ways: exp integral ∫a^(bx+c) dx
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4 ways: exp integral ∫a^(bx+c) dx

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Any function f is a sum of an EVEN & an ODD function
3:33

Any function f is a sum of an EVEN & an ODD function

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2 ways: integral ∫x/(x+a) dx
2:18

2 ways: integral ∫x/(x+a) dx

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exp derivative e^f(g(x)) h(x)
1:31

exp derivative e^f(g(x)) h(x)

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Alternate way: Evaluate exp sq root integral ∫a^x/√(1-a^(2x)) dx
0:51

Alternate way: Evaluate exp sq root integral ∫a^x/√(1-a^(2x)) dx

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2nd/2parts example Show Σk^2 = ΣΣmin(i,j) where i,j,k=1 to n
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2nd/2parts example Show Σk^2 = ΣΣmin(i,j) where i,j,k=1 to n

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1st/2 ways: derivative x^2/3 + y^2/3 = a^2/3
1:16

1st/2 ways: derivative x^2/3 + y^2/3 = a^2/3

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Princeton U: Compute the integral ∫sin^5(x)/cos(x) dx
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Princeton U: Compute the integral ∫sin^5(x)/cos(x) dx

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exp derivative (log f(ax+b) (g(cx+d)))^h(mx+n)
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exp derivative (log f(ax+b) (g(cx+d)))^h(mx+n)

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