Project ForgeEngineering Mathematics
Calculus
GATE 2020
Hard
The value of lim(x→1) [(1−e^(−c(1−x))) / (1−x·e^(−c(1−x)))] is
- Ac
- Bc+1
- c/(c+1)
- D(c+1)/c
Explanation
Substitute t=1−x→0. Numerator: 1−e^(−ct) ≈ ct − c²t²/2. Denominator: 1−(1−t)e^(−ct) ≈ 1−(1−t)(1−ct) = t(1+c) − ct² (to matching order). The ratio → [ct(1−ct/2)] / [t((1+c)−ct)] → c/(1+c) as t→0.
Source: GATE ME 2020 Session 1 (ME-1) (2020)
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.