2nd way: exp integral e^3x/(e^x +2) dx withOUT u-sub

example: Mean, Median & Mode

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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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This world is just one big makeshift operation—time to quickly debunk the so-called “big shots.”

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Review: Multiplying each obs. by a CONSTANT results in new variance =

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prob stat: A population of N=5 scores has a mean µ= 12. What is ∑X for this sample?

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AP Calculus 2nd way: integral ∫ (3^(x+1)-7^(x-1))/21^x dx

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Find the area via Pick's Theorem

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

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

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prob stat The events A & B are s.t P(A)=5/12, P(B)=2/3 & P(A' n B')=1/12.

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Variability or spread of a distribution. Whey we need it!

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AP Calculus 3rd way: exp integral 1/(1+e^x) dx [withOUT u-sub]

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derivative If y=(a+bx)e^(-nx), prove that y2+2ny1+n^2y=0

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UC Davis #22 [THE INTEGRATION OF RATIONAL FUNCTIONS] withOUT u-sub

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#19 2011 MIT Integration Bee Qualifying Exam

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AP Calculus 4th way: exp ∫1/(1+e^x) dx via 3rd u-sub

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Screen Recording 2023-12-07 at 2.04.49 AM

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2nd way: exp integral ∫e^(1/x)/x^2 dx

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prob stat: 2 ways Joe's mean mark for the physics tests for the term was 72.

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Lamar U: #11 trig integral ∫csc^6(x/4) cot^4(x/4) dx

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