problem archive
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Find the second derivative of the function $f(x) = 4x^3 - 2x^2 + 5$ -
Evaluate the integral $\int e^{2x} \sin(x) \,dx$ -
Find the limit $\lim_{{x \to \infty}} \left(1 + \frac{3}{x}\right)^x$ -
Compute the derivative of $g(x) = \cos^2(x) + \tan(x)$ -
Evaluate the definite integral $\int_{0}^{\pi/2} \cos(x) \,dx$ -
Determine the derivative of $h(x) = \frac{1}{x} + e^x$ -
Find the limit $\lim_{{h \to 0}} \frac{{f(4 + h) - f(4)}}{{h}}$ given $f(x) = \sqrt{x} + 2x$ -
Calculate the area under the curve $y = \sin(x)$ from $x = 0$ to $x = \pi$ -
Find the derivative of $f(x) = \ln(x) + x^2$ -
Evaluate the improper integral $\int_{1}^{\infty} \frac{1}{x} \,dx$ -
Calculate the absolute value (modulus) of the complex number $w = -2 - 5i$ -
Find the square root of the complex number $z = 4 + 3i$ -
Find the product of the complex numbers $z = 2 + i$ and $w = 1 - 3i$ -
Find all solutions to the equation $z^2 = -4$ in the complex plane -
Express the complex number $z = -1 + i$ in polar form -
Compute the conjugate of the complex number $w = 3 - 2i$ -
Determine the argument (angle) of the complex number $z = 1 + \sqrt{3}i$ -
Find the roots of the quadratic equation $z^2 + 2z + 5 = 0$ in the complex plane -
Evaluate the expression $e^{i \pi}$ using Euler's formula -
Solve the equation $z^3 = 8$ in the complex plane