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If u=a+ib is a complex #, then complex conjugate of u*=a-ib. ...
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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
1st way: exp ∫(e^x)/x (1+x log(x)) dx
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An Overpowered Undead Ruler Conquers a New World Part 2
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UC Davis #16: Prove (fgh)'=f'gh+fg'h+fgh' [differentiation using the product rule]
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sum picture proof show 1^2+2^2+3^2+...+n^n=1/3 1/2n(1+n) (2n+1)
Which pairs are equivalent via truth table?
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#9 2023 MIT Integration Bee Qualifying Exam
Bijection of elements in tn & a pair of elements of (n+1)
#17 2011 MIT Integration Bee Qualifying Exam
picture "proof":Show Σk^2 = ΣΣmin(i,j) where i,j,k=1 to n
hotel booking class 05 part 02
2nd way: integral tan(x)/(1+tan(x)) dx
#9 2010 MIT Integration Bee Qualifying Exam
U Penn: Evaluate trig integral ∫(sin^2(x) -cos^2(x))/(sin(x)-cos(x))^2 dx
#1 2017 MIT Integration Bee Qualifying Exam
review: prob stat Population variance vs sample variance
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Alternate way: 2nd picture Show 1+3+5+...+(2n-1)=n^2
Section 1- Before web dev Journey, Lecture 2- Meet your Instructor - Hitesh