5th/5ways: triangular num: Show t(n-1) + tn = n^2 where tn = nth triangular number

New version#Golden Legend#Teacher's contrasting perspective 55.81

yishupinjianwu

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

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Pantun Melayu [Pulau Pandan Jauh Ke Tengah]

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

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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx

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

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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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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mangzhongne

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2 ways: exp derivative ln(e^(x+1/x))

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1st/2 ways: derivative x^2/3 + y^2/3 = a^2/3

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

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Suppose E & F are mutually exclusive events. Must E & F be complementary? Explain your answer.

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2nd way: derivative ∫log (f(x))^g(x) (p(x))^r(x)

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

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2nd way: trig integral ∫√(sec^5(x)/sin^3(x)) dx

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implicit differentiation Find dy/dx, sin(xy) +x/y = x^2 -y

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Given events J & K:

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2nd way: sq rt integral ∫(√x)/(x+1) dx

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

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