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Every continuous function f defined on \([a, b]\) is Riemann integrable

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40 Maths General Knowledge Questions And Answers

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Every continuous function f defined on \([a, b]\) is Riemann integrable

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A bounded function \( f:[a, b]\to \mathbb{R} \) is Riemann integrable iff for every \( \epsilon>0 \) there exist a partition \( P_\epsilon \) of [a, b] such that \( U(f, P_\epsilon)-L(f, P_\epsilon)<\epsilon. \)

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Find the value of k, for which $f(x)=\begin{cases} \frac{\sqrt{1+kx}-\sqrt{1-kx}}{x}, \text{if} \ -1\le x<0 \\ \frac{2x+1}{x-1}, \text{if} \ 0\le x<1 \end{cases}$ is continuous at x=0.

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Every continuous function f defined on \([a, b]\) is Riemann integrable

40 Maths General Knowledge Questions And Answers

Continuous image of connected set is connected

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