UC Davis #11: count prove Σi^2 = n(n+1)(2n+1)/6 where i=1 to n

multivariable Let f(x,y)=4-2xx^2-y^2. Find the slope of the tangent line at the point (1,1,1)...

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

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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(x)) dx

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2 ways: trig integral cos^2(x) sin^2(x) dx

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Screen Recording 2024-05-19 at 9.41.57 PM

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1) integral ∫1/5 dx/(1+x) vs 2) integral ∫sec^(5x)/(1+ tan(5x)) dx

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2 ways: trig integral ∫tan^3(x) sec^2(x) dx

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prob stat One of the longest words in std. statistics terminology is "HOMOSCEDASTICITY".

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

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JEE Main integral x^2/(a+bx)^2 dx

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Rutgers U: 2nd way compute ∫√(x^2 -2)/x dx

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Lamar U 2nd way: evaluate exp integral ∫e^(2x)/(1+e^(2x)) dx

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2 ways: integral ∫(a^2-x^2) dx

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U Penn: Show that the following decomposition CANNOT hold ...

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#12 UC Davis: Find the length of the graph for x=ln(y)=y^2/8 on the closed interval ...

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A bag contains 5 red balls & 3 green balls. A ball is selected at random &

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prob stat 2/2 ways: A couple has 6 children whose ages are 6,8,10,12,14,16.

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prob stat a) Calculate the mean & the std deviation of 4 numbers 2,3,6,9

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1) integral ∫x/(1+x) dx vs 2) integral ∫sin(x) cos(x)/(1+ sin(x)) dx

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U Arizona: For each integral decide which of the following is needed:

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