What is lim f 39 x equal to x rarr ...........

Mathematics (NDA) limits

Consider the following for the next three (03) items that follow :

Let f' (x) = | cos x x 1 |

| 2sin x x² 2x |

| tax x x 1 |

What is lim f'(x) equal to ?

x→ x

This questions was previously asked in

2023 NDA -1 Math

-1

- You have a matrix function, f'(x), indicated with elements involving trigonometric functions and polynomials.

- The determinant of this 3x3 matrix f'(x) at x ? x needs to be calculated.

- Calculate the determinant:

- | cos x x 1 |

- | 2sin x x^2 2x |

- | tanx x x 1 |

- Substituting x into these elements:

- | 1 x 1 |

- | 0 x^2 2x |

- | 0 x 1 |

- Solve this determinant to find the limit.

- As x ? x, the determinant simplifies and the calculation yields 0.

Correct Answer: Option 2 - 0

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