GATE 2020 BT – Question 27

Engineering Mathematics · Calculus: Limits, continuity, differentiability, partial derivatives, maxima and minima · 1 mark · Numerical answer

A function is given by $$f(x)=\begin{cases}15,&x<1,\\cx,&x\ge1.\end{cases}$$ Find the integer c for which f is continuous.

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Correct answer: 15 to 15

Explanation

Both pieces are continuous within their own intervals. At the junction x = 1, the left limit is 15 and the value and right limit are c. Continuity requires $c=15$, which also makes the two limits agree with f(1).

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