1st/3 ways: Show 1+2+3+...+n=n(1+n)/2 via picture

STPM Math T Sem. 2: Ex 11.2 Given that f(x)=tan(x), show that ...

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Penn. State U: Suppose the p.m.f of discrete random variable X is ...

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🪔 Happy Deepavali 🪔 [Nov-12-2023]

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lim x/e^x? as x→∞

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exp Differentiate (i) b^e^x (ii) b^x&e (iii) (b^e)^x (iv) (b^x)^e

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

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Alternate way: sq root integral ∫1/√((x-α)(x-β)) dx

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121 122

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#5 MIT 2022 Integration Bee Qualifying Exam

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Pascal's triangle nth triangular number [examples]

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Lamar U: Use log. differentiation to find the 1st derivative of the given function

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3 ways: If y=x/(1+x^2) find dy/dx.

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exp integral e^2x/(1+e^x) dx

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1st/2ways: permutation Show P(n,2)+P(n,1)=n^2

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#16 MIT 2022 Integration Bee Qualifying Exam

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Texas Tech: Find integral #7 ∫xsin(x^2) dx vs #5 ∫xsin^2(x) dx

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Alternate way: 2nd picture Show 1+3+5+...+(2n-1)=n^2

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logic: tautology p→q≡(¬q→¬p)

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commutative: ab=ba via "picture"

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A random variable X has the following parameters: E(X)=a & Var(X)=2a^2-1 a∈R

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