Question
Consider the following for the two (02) items that follow: Let the function f(x) = x^2 + 9. What is _ x 0 f(x) - 3 f(x)+7 - 4 equal to?
NDA
Mathematics
Limits
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. 2 3
- B. 1
- C. 4 3
- D. 2
Answer
C. 4 3
Step-by-step solution
Given f(x) = x^2 + 9. The limit is _ x 0 x^2 + 9 - 3 x^2 + 16 - 4 . Rationalizing the numerator and the denominator: _ x 0 ( x^2 + 9 - 3)( x^2 + 9 + 3) ( x^2 + 16 - 4)( x^2 + 16 + 4) x^2 + 16 + 4 x^2 + 9 + 3 _ x 0 x^2 + 9 - 9 x^2 + 16 - 16 x^2 + 16 + 4 x^2 + 9 + 3 _ x 0 x^2 x^2 x^2 + 16 + 4 x^2 + 9 + 3 Cancelling x^2 and substituting x = 0: 16 + 4 9 + 3 = 4 + 4 3 + 3 = 8 6 = 4 3 Answer: 4 3
Related: Mathematics — Limits · All PYQ Banks