Growing patterns #2

Iowa State U [Fall 2019]: integral Find the integral

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diff eq: Solve dy/dx = (2y4x^4)/(xy^3) ❌separable to ✅separable

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2 ways: sq root derivative 1/(√√(1/√x))

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

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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)

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

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

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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx

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1st/2ways: logic Import-Export

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AP Calculus: integral ∫(5√x^3 + √6x) /√x dx

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2nd way: integral ∫(6+4x--2x^2) dx via 1) complete sq 2) then trig. sub

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Lamar U: Derivatives of Exponential & Log Functions Practice Problems.

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prob stat: The speeds, to the nearest mile per hour,, of 120 vehicles passing a check point

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alternate way: count sum 1 + 2 + 3+... + n via "polynomial"

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UT Austin: trig integral ∫(1/x^2) sin(1/x) cos(1/x) dx

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Screen Recording 2024-02-22 at 10.30.06 PM

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Prove Σ1/((k-1)(k+1))=(3n^2-n-2)/(4n(n+1)) where k=2 to n ∀n ≥ 2

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trig integral ∫sec^2(x)/tan(x) dx vs ∫tan(x)/sec^2(x) dx

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Prove the slope-intercept formula by using the slope formula for the line that has slope m, ...

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1st/2 parts: Inverse 2x2 matrix

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