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...

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 01 Let \(x = \dfrac{3 + \sqrt{3}}{3 - \sqrt{3}}\) and \(y = \dfrac{3 - \sqrt{3}}{3 + \sqrt{3}}\). If...

QUESTION 02 The roots of the equation \(x^3 - x^2 - 10x - 8 = 0\) are \(x_1, x_2,\)...

QUESTION 03 The sum of all solutions to the equation \(2 \sin^2 x - \cos x = 1\) for...

QUESTION 04 Solve the equation \(2^{2x+2} + 3 \cdot 2^{x} - 1 = 0\). \(x = \) 🔍 Solution...

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QUESTION 06 Let \(O(0,0)\), \(A(1,1)\) and \(B(x,-1)\). The positive value of \(x\) such that \(\angle AOB = \dfrac{\pi}{3}\) can...

QUESTION 07 Find the radius of the sphere \(x^2 + y^2 + z^2 = 2x + 6y - 1\)....