Computer Sciences > GATE 2026 SET-1 > Calculus
f(n) = c1ex − c2 log(1/x), x > 0
f(n) = 3, otherwise
If f is continuous at x = 0, then the value of c1 + c2 is ______ (integer).
f(n) = 3, otherwise
If f is continuous at x = 0, then the value of c1 + c2 is ______ (integer).
Correct : 3
For f to be continuous at x = 0, the limit as x → 0 must equal f(0) = 3
limx→0+ f(x) = limx→0+ [c1ex − c2 log(1/x)]
As x → 0+:
ex → 1
log(1/x) = −log(x) → +∞
For the limit to exist and equal 3, the log term must vanish.
So c2 = 0 to eliminate the diverging term.
With c2 = 0:
limx→0+ c1ex = c1 × 1 = c1
For continuity: c1 = 3
c1 + c2 = 3 + 0 = 3
The value of c1 + c2 = 3
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