QUESTION 06 How many integers \(n\) are there such that \(1 \le n \le 200\) and \(n\) is not...

QUESTION 07 Let \(\vec{a}=(1,3,-2)\), \(\vec{b}=(2,1,1)\), and \(\vec{c}=(-3,1-s,t)\). If \(\vec{c}\) is perpendicular to both \(\vec{a}\) and \(\vec{b}\), find the value...

QUESTION 08 The equation of the tangent to the curve \(y = e^{\frac{x}{2}}\) that passes through the origin \((0,0)\)...

QUESTION 09 The sequence \(\{a_{n}\}\) satisfies the following conditions: \ Calculate the sum of the...

QUESTION 10 \ Find the value of \(k\). 🔍 Solution \begin{equation*} \begin{split} & \text{1. Method 1:...

QUESTION 11 Let \(f(x) = x - \ln(2x+1)\). Solve the inequality \(f'(x) < 0\). If the solution is in...

QUESTION 12 Calculate the definite integral: \ The value of the integral can be...

QUESTION 13 Let \(A = a \begin{pmatrix} 1 & -1 \\ 1 & 1 \end{pmatrix}\) with \(a > 0\),...

QUESTION 14 Let \(n\) be a positive integer. Answer the following questions. (A) Let \(f(x) = x(1-x)^n\). The solution...

QUESTION 01 The roots of the equation \(x^{3} + 4x^{2} + 4x + 1 = 0\) are \(x_1, x_2,\)...