Calculus Questions Set 2:
What does k = limx→0 (xx - ax) / (xa - aa) evaluate to?
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What is the value of limx→π/2 (log(sin(x))/(π/2 - x)^2)?
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Find the limit of tan(y)/x as (x, y) approaches (0, 0).
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What is the slope of the tangent of the polar curve: r = a(1 + cos θ)?
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What is the angle of intersection of the curves r = sin(θ) + cos(θ) and r = 2sin(θ)?
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Differentiation of x3 / (1 - x3) with respect to x3 is
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Let f(x) = limit of n(x^(1/n) -1), x>0 as n approaches to ∞, then find f(xy).
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What is the angle between the radius vector and the tangent for the following polar curve: r = a(1 - cos θ)?
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Let f(x) = 3x10 - 7x8 + 5x6 - 21x3 + 3x2 - 7. Find the value of lim (f(1-h) - f(1)) / (h3 + 3h) as h → 0.
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Find the solution for the differential equation dx/dt + 2x(t) = δ(t) with initial condition x(0) = 0 using Laplace transformation.
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