The Maclaurin series of an EVEN function includes only EVEN powers.

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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logic Idempotent law show x=xVx

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🪔 Happy Deepavali 🪔 [Nov-12-2023]

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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2nd way: integral ∫ log √x(x^n) dx

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UC Davis #16: Prove (fgh)'=f'gh+fg'h+fgh' [differentiation using the product rule]

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implicit differentiation Find dy/dx, sin(xy) +x/y = x^2 -y

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derivative (f(x)/g(x))^h(x)

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UC Davis#2: 2nd way integral ∫(2x+3)/(x^2-9) dx [integration by partial fraction]

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2nd/2 ways: Show 1+3+5+ ... +(2n-1) + (2n+1) + (2n-1)+...+5+3+1= n^2 + (n+1)^2

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Find the area via Pick's Theorem

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Screen Recording 2024-02-02 at 1.54.05 AM

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integral ∫(8x+12) (x^2+3x+1)^4 dx vs integral ∫(8x+12)/(x^2+3x+1)^4

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Alternate way: 2nd picture Show 1+3+5+...+(2n-1)=n^2

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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/2 ways: [k-map] logic:Simplify the Boolean function F=A+A'B

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Roorkee 1976 RET 1991Hindustan: trig integral 1/(sin^2(x) cos^2(x)) dx

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#8 Lamar U: evaluate integral sec^8(t/2) tan^5(t/2) dt

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