Project ForgeEngineering Mathematics
Calculus
GATE 2008
Medium
lim (x→∞) (x − sin x) / (x + cos x) equals:
- 1
- B−1
- C∞
- D−∞
Explanation
Divide numerator and denominator by x: (1 − sin(x)/x) / (1 + cos(x)/x). Since sin(x) and cos(x) are bounded between −1 and 1, both sin(x)/x and cos(x)/x → 0 as x→∞. The limit is therefore (1−0)/(1+0) = 1.
Source: GATE CS 2008 (2008)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.