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Ex11.6 STPM Math T Sem.2 Find the fir st 4 terms in the expansion of the following functions
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If y=acos(ln(x)) + bsin(ln(x)), show that x^2y2 + xy1 +y=0
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Vandermonde's Identity
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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx
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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx
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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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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx
AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(x)) dx
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UC Davis#4 4 ways: integrate 7^(2x+3) dx
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example Find 1+2+3+...+n via Pick's Theorem
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3 ways: derivative a^(f(x)g(x))
Alternate way: log integral ∫1/(x+xln(2x))
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3 ways: ∫ (3x+11)/(x^2-x-6) dx
Screen Recording 2023-12-06 at 3.07.30 AM
Show log b^n(x^m) = m/n logb(x)
Review: integral ∫1/(x^2-a^2)dx vs integral ∫1/(a^2-x^2) dx vs integral ∫1/(x^2+a^2) dx
We lost original x's but still know mean x̄ & n. Now we collected m new observations.
1st/2parts: Linear interpolation (2 given points)
prob stat Toss a pair of fair 6-sided dice. The sample space has 36 outcomes.
2 ways: Derivative √ (1+√ (1+√ x)))