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...

QUESTION 04 The solution to the inequality \(\log_{2}\sqrt{2x-1} < \log_{4}x\) is in the form \(a < x < b\)....

QUESTION 05 Evaluate the sum: \ 🔍 Solution \begin{equation*} \begin{split} & \text{1. Rationalize the denominator of the general term:}...

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:...