problem archive
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Calculate the dot product of vectors $\mathbf{u} = \langle 3, -1, 2 \rangle$ and $\mathbf{v} = \langle 2, 4, -1 \rangle$ -
Apply the linear transformation $T(x, y) = (4x + 2y, 3x - y)$ to the vector $\langle -1, 2 \rangle$ -
Find the inverse of matrix $G = \begin{bmatrix} 2 & 1 \\ 4 & 3 \end{bmatrix}$ -
Solve for x: $5x - 2 = 3$ -
Determine the eigenvalues and eigenvectors of matrix $H = \begin{bmatrix} 1 & 0 \\ 2 & 3 \end{bmatrix}$ -
Factor the quadratic expression: $2x^2 + 3x + 1$ -
Find the solution to the system of equations: $3x + y = 6$, $2x - 4y = -5$ -
Find the inverse of matrix $I = \begin{bmatrix} 3 & 2 \\ -1 & 4 \end{bmatrix}$ -
Calculate the dot product of vectors $\mathbf{u} = \langle -2, 1, 3 \rangle$ and $\mathbf{v} = \langle 4, 2, -1 \rangle$ -
Multiply the matrices: $A = \begin{bmatrix} 1 & 2 \\ 0 & -1 \end{bmatrix}$, $B = \begin{bmatrix} 3 & -1 \\ 2 & 4 \end{bmatrix}$ -
Evaluate the integral $\int (2x + 5) \,dx$ -
Find the derivative of the function $f(x) = 3x^2 - 2x + 1$ -
Find the limit $\lim_{{x \to 2}} \frac{{x^2 - 4}}{{x - 2}}$ -
Evaluate the definite integral $\int_{0}^{1} (x^2 + 2x) \,dx$ -
Find the limit $\lim_{{h \to 0}} \frac{{f(3 + h) - f(3)}}{{h}}$ given $f(x) = x^2 - 2x + 1$ -
Compute the derivative of $g(x) = \sin(3x)$ -
Calculate the area under the curve $y = x^2$ from $x = 0$ to $x = 2$ -
Find the derivative of $f(x) = \sqrt{x} + 2x^3$ -
Determine the derivative of $h(x) = e^{2x} + \ln(x)$ -
Evaluate the improper integral $\int_{1}^{\infty} \frac{1}{x^2} \,dx$