Suppose z is differentiable funtion of x & y that is defined implicitly x^2+y^3-z+2yz^2=5

logic Idempotent law show x=xVx

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Always ZERO

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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(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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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: trig integral ∫sin(x/a) dx

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When a die was thrown the scores was an odd #. What is the prob. that it was a prime #?

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trig Show sec^4(x)-tan^4(x) = sec^2(x)+tan^2(x)

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2 ways: integral ∫(a^2-x^2) dx

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2nd way: integral ∫a^log√a(x^n) dx

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Screen Recording 2023-12-07 at 2.04.49 AM

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U Penn: Show that the following decomposition CANNOT hold ...

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