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Evaluate the limit as x approaches 0 of (sin(3*x) - 3*x) / x**3.
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-9/2
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from sympy import symbols, limit, sin
x = symbols('x')
expr = (sin(3*x) - 3*x) / x**3
result = limit(expr, x, 0)
print(result)
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Evaluate the definite integral of (1 - x**2)**3 from x = 0 to x = 1.
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16/35
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from sympy import symbols, integrate
x = symbols('x')
expr = (1 - x**2)**3
result = integrate(expr, (x, 0, 1))
print(result)
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Evaluate the limit as n approaches infinity of n*(sqrt(n**2 + 1) - n).
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1/2
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from sympy import symbols, limit, sqrt
n = symbols('n', positive=True)
expr = n*(sqrt(n**2 + 1) - n)
result = limit(expr, n, float("inf"))
print(result)
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Compute the sum of the series sum from n = 1 to 50 of 1/(n*(n+1)).
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50/51
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from sympy import symbols, summation
n = symbols('n', positive=True, integer=True)
expr = 1/(n*(n+1))
result = summation(expr, (n, 1, 50))
print(result)
|
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