Consider the function f : R R defined as follows: f(x) = cases c_1 e^x - c_2 _e≤ft(1x), & if x > 0 \\ 3, & otherwise cases where c_1, c_2 ∈ R. If f is continuous at x = 0, then c_1 + c_2 = _________. (answer in integer)

GATE CSE 2026 Session 1 Q32: Continuity at 0 of c1·e^x − c2·ln(1/x)

Consider the function $f : \mathbb{R} \to \mathbb{R}$ defined as follows:

$f(x) = \begin{cases} c_1 e^x - c_2 \log_e\left(\dfrac{1}{x}\right), & \text{if } x > 0 \\ 3, & \text{otherwise} \end{cases}$

where $c_1, c_2 \in \mathbb{R}$ .

If $f$ is continuous at $x = 0$ , then $c_1 + c_2 =$ _________. (answer in integer)

Try it: numerical answer: type the value

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Answer: 3 (official GATE 2026 final answer key)

Concept used: Continuity needs the right-hand limit to be finite and equal to $f(0)$ .

First step: As $x \to 0^+$ , $\log_e(1/x) \to \infty$ , so the limit is finite only if $c_2 = 0$ ; then match $c_1$ to $f(0) = 3$ .

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Source: official GATE 2026 Session 1 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key