Exams › JEE Main › Maths

If f(x) = | cos x x 1 | | 2 sin x x² 2x | | tan x x 1 |, then lim x→0 f'(x)/x

1. exists and is equal to −2
2. does not exist
3. exist and is equal to 0
4. exists and is equal to 2

Correct answer: exists and is equal to −2

Solution

The limit of f'(x)/x as x approaches 0 exists and equals -2 because the derivative of the matrix function f(x) can be computed using the properties of derivatives and the behavior of trigonometric functions near zero, leading to a consistent result.

Related JEE Main Maths questions

• If [ ] represents the greatest integer less than or equal to the given real number, and -1 ≤ x < 0, 0 ≤ y < 1, 1 ≤ z < 2, then the determinant [x] [y] [z] [x+1] [y+1] [z] [x] [y] [z]+1 is equal to:
• Let x, y and z be complex numbers. If Δ denotes the determinant of the matrix [0, -y, -z; y, 0, -x; z, x, 0], then Δ is
• For the linear system x1 + 2x2 + 3x3 = 6 x1 + 3x2 + 5x3 = 9 2x1 + 5x2 + ax3 = b if it is consistent and admits infinitely many solutions, then which statement must be true?
• For which value(s) of x does the determinant of the matrix | 1 (x−3) (x−3)² | | 1 (x−4) (x−4)² | | 1 (x−5) (x−5)² | become zero?
• Let Δ_r denote the determinant [2r-1, {^mC_r}, 1; m²-1, 2^m, m+1; sin²(m²), sin²(m), sin²(m+1)]. Then the value of ∑_(r=0)^(m) Δ_r is
• If the determinant expression [a, b, ax+by; b, c, bx+cy; ax+by, bx+cy, 0] is considered under the conditions b²-ac<0 and a<0, what is its sign?

⚔️ Practice JEE Main Maths free + battle 1v1 →