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#2 2012 MIT Integration Bee Qualifying Exam

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multivariable partial Let w=2x^2 y, where x=u^2+v^2 & y=u^2-v^2. Find ∂w/∂u & ∂w/∂v.
2:04

multivariable partial Let w=2x^2 y, where x=u^2+v^2 & y=u^2-v^2. Find ∂w/∂u & ∂w/∂v.

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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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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
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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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2nd way: integral ∫ log √x(x^n) dx
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2nd way: integral ∫ log √x(x^n) dx

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

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

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1st/2ways: Find the sum 1/7, 10/21, 17/21, 24/21, 31/21 via median.
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1st/2ways: Find the sum 1/7, 10/21, 17/21, 24/21, 31/21 via median.

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UC Davis #11: count prove Σi^2 = n(n+1)(2n+1)/6 where i=1 to n
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UC Davis #11: count prove Σi^2 = n(n+1)(2n+1)/6 where i=1 to n

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

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sum Find 1/1.4 + 1/4.7 +1/7.10+... +1/((3n-2)(3n+1))
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sum Find 1/1.4 + 1/4.7 +1/7.10+... +1/((3n-2)(3n+1))

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UC Davis #16: Prove (fgh)'=f'gh+fg'h+fgh' [differentiation using the product rule]
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UC Davis #16: Prove (fgh)'=f'gh+fg'h+fgh' [differentiation using the product rule]

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The sum of 3 numbers in AP is 15 & the sum of their squares is 3. Find the numbers.
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The sum of 3 numbers in AP is 15 & the sum of their squares is 3. Find the numbers.

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2 ways: Find logarithm of 5 to the base 5 √5.
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2 ways: Find logarithm of 5 to the base 5 √5.

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Calculus: Find nth derivative of log(ax+b)
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Calculus: Find nth derivative of log(ax+b)

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How did “Chinese specialties” ignite European culture?
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How did “Chinese specialties” ignite European culture?

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MPPET 1993 BIT Ranchi 1982 Hindusta: trig integral ∫ (1+cos^2(x)/sin^2(x) dx
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MPPET 1993 BIT Ranchi 1982 Hindusta: trig integral ∫ (1+cos^2(x)/sin^2(x) dx

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

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AP Calculus 2nd way: integral ∫(ax+c)/(ax^2 + bx) dx
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AP Calculus 2nd way: integral ∫(ax+c)/(ax^2 + bx) dx

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prob stat: A group consists of 4 girls & 7 boys. In how many ways can a team of 5 members ...
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prob stat: A group consists of 4 girls & 7 boys. In how many ways can a team of 5 members ...

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OSU Math 1151 Practice4: Compute the derivative
9:26

OSU Math 1151 Practice4: Compute the derivative

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