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 \(x_1, x_2,\)...

QUESTION 02 The sum of all solutions to the equation \(\cos 2x + \cos x = 0\) for \(0...

QUESTION 03 The solution to the inequality \(3^{x+1} + \dfrac{1}{3^x} < 4\) is in the form \(a < x...