Find the mean 118,50,84,67,101 withOUT calculation. Support your answer.

#17 2011 MIT Integration Bee Qualifying Exam

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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

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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

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Bijection of elements in tn & a pair of elements of (n+1)

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#9 2023 MIT Integration Bee Qualifying Exam

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#9 2010 MIT Integration Bee Qualifying Exam

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2nd way: integral tan(x)/(1+tan(x)) dx

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sum picture proof show 1^2+2^2+3^2+...+n^n=1/3 1/2n(1+n) (2n+1)

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If u=a+ib is a complex #, then complex conjugate of u*=a-ib. ...

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UC Davis #10: count prove Σi = n(n+1)/2 where i=1 to n

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

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Section 1- Before web dev Journey, Lecture 2- Meet your Instructor - Hitesh

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#5 2020 MIT Integration Bee Quali Exam: integral 1/(x^2+(x-1)^2) dx

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#24 2010 MIT Integration Bee Qualifying Exam

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Which pairs are equivalent via truth table?

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8Screen Recording 2023-12-07 at 1.55.57 AM

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picture "proof":Show Σk^2 = ΣΣmin(i,j) where i,j,k=1 to n

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

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