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Preview of Math Certification Answers
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Summary

There are no integer solutions (x, y) for 7x^2 - 9y^2 = 391.
f(x) is differentiable for all real numbers x and its derivative function f'(x) is continuous.
The sum of the series ∑[n=1 to ∞] (-1)^(n+1)/n = -π/ln(2).
α^2 + β^2 + γ^2 = 0.
ℓ = √((|α|^2 + |β|^2 + |γ|^2)/2).
The confidence interval is 14.87 ≤ m ≤ 15.13 or 14.96 ≤ m ≤ 15.04.
The area of △SPP' can be expressed as (1/2)SP ΔP sin(π - θ).
tr(AB) = tr(BA).
tr(A) = tr(A^2) = … = tr(A^n) = 0.
An = O.
f does not contain the xyz-term, x^3-term, y^3-term, or z^3-term.
f has the form f = ax^2y + bxy^2 + cy^2z + dyz^2 + pz^2x + qzx^2.
∂^2f/∂x^2 + ∂^2f/∂y^2 + ∂^2f/∂z^2 = 2ay + 2qx.

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There are no integer solutions (x, y) for 7x^2 - 9y^2 = 391.
f(x) is differentiable for all real numbers x and its derivative function f'(x) is continuous.

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