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3 ways: sum Show 1+3+5+...nth term = n^2
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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) 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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2nd way: Find dy/dx a)x^y=y^x b)x^y+y^x=(x+y)^(x+y c) (cos(x))^y=(sin(y))^x
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2 ways: ∫ 1/(10x^2 -x-21) dx
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Screen Recording 2024-05-05 at 11.28.23 PM
9Screen Recording 2023-12-02 at 2.43.56 AM
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Find the expected value & the variance of a geometric r.v. X
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2Screen Recording 2024-05-17 at 6.10.36 PM
2nd/2 ways: exp log integral ∫e^(n ln(x)) dx
prob stat The events A & B are s.t P(A)=5/12, P(B)=2/3 & P(A' n B')=1/12.
integration bee 2014 UNSW 2nd way: tan(x)/(sin(x) cos(x)) dx
Screen Recording 2023-12-02 at 3.42.17 AM
2nd way: log hyper trig derivative ln(tanh(2x))