Using first principle, find the derivative of loge x where x ∈ (0, ∞).

Find the rank of the matrix A = ⎡ 2 3 7 ⎤
⎣ -2 4 1 ⎦
⎢ -3 -1 ⎥ by reducing into echelon form.

For x∈(−1,1)], the number of solutions of the equation arcsin x = 2 arctan is equal to ____.

Prove the following: cosA + sinA cosA - sinA - cosA - sinA cosA + sinA = 2 tan 2A

Which of the following is a null set:

• A {0}
• B {x: x > 0 or x < 0}
• C {x: x² = 4 or x = 3}
• D {x: x² + 1 = 0, x ∈ R}