Question
If the function f(x)= e^ x (e^ x-x -1 )+ _ e ( x+ x)-x x-x is continuous at x=0, then the value of f(0) is equal to
JEE Main
Mathematics
Continuity and Differentiability
2026
JEE Main 2026 (24 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 2 3
- B. 2
- C. 3 2
- D. 1 2
Answer
C. 3 2
Step-by-step solution
f(0) = _ x 0 e^ x - e^x + ( x + x) - x x - x Applying L'hospital rule f(0) = _ x 0 e^ x ^2 x - e^x + x - 1 ^2 x - 1 f(0) = _ x 0 e^ x ( ^2 x - 1) + (e^ x - e^x) + x - 1 ^2 x f(0) = _ x 0 ( e^ x + e^x ( e^ x - x - 1 ) ^2 x + 1 x + 1 ) f(0) = 1 + 0 + 1 2 = 3 2
Related: Mathematics — Continuity and Differentiability · All PYQ Banks