Project ForgeEngineering Mathematics
Calculus
GATE 2016
Medium
Lt(x→0) [loge(1+4x)] / (e^(3x) - 1) is equal to
- A0
- B1/12
- 4/3
- D1
Explanation
Applying L'Hopital's rule (0/0 form): d/dx[loge(1+4x)] = 4/(1+4x) → 4 at x=0. d/dx[e^(3x)-1] = 3e^(3x) → 3 at x=0. Limit = 4/3.
Source: GATE ME 2016 Set-3 (2016)
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