QUESTION 05 The solution of the inequality \((\log_{3}x)^{2} < \log_{9}x^{4}\) is in the form of \(a < x <...

QUESTION 06 The solution of the inequality \(\sin 2x > \sqrt{2} \sin x\) for \(0 \le x < 2\pi\)...

QUESTION 07 Let \(\vec{a} = (1,2,3)\), \(\vec{b} = (3,2,1)\), and \(\vec{c} = (5,4,3)\). Find the value of \(t\) such...

QUESTION 08 Let \(O(0,0)\) and \(A(3,1)\). Let \(A'\) be the symmetric point of \(A\) with respect to the line...

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

QUESTION 10 Given \(\displaystyle \lim_{x\rightarrow\infty}(\sqrt{x^{2}+4x+5}-\sqrt{x^{2}+x}) = p\). Find the value of \(2p\). 🔍 Solution \begin{equation*} \begin{split} & \text{1. Multiply...

QUESTION 11 Let \(f(x) = \dfrac{\cos x}{\sqrt{e^x}}\). Calculate the value of \(2 \cdot f'(0)\). 🔍 Solution \begin{equation*} \begin{split} &...

QUESTION 12 Evaluate the definite integral: \ 🔍 Solution \begin{equation*} \begin{split} & \text{1. Use...

QUESTION 13 Let \(I = \begin{pmatrix} 1 & \\ & 1 \end{pmatrix}\) and \(O = \begin{pmatrix} & 0 \\ 0 & 0 \end{pmatrix}\). (A) Let \(A = \begin{pmatrix} 1 & 3 \\ 3 & 5 \end{pmatrix}\) and \(B = \begin{pmatrix} x & 3 \\ 3 & 6 \end{pmatrix}\). Find the value of

QUESTION 14 Answer the following questions regarding definite integrals. (A) The definite integral \(\displaystyle \int_{0}^{\frac{\pi}{4}}\cos^{2}x \, dx\) can be...