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Ashwini Shirsat on A woman starts shopping with Rs. X and Y paise, spends Rs. 3.50 and is left with Rs. 2Y and 2X paise. The amount she started with is
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Naresh Patkare on 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.
Ashwini Shirsat on 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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Unknown on 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 ​\( U(f, P_\epsilon)-L(f, P_\epsilon)<\epsilon. \)
Naresh Patkare on 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 ​\( U(f, P_\epsilon)-L(f, P_\epsilon)<\epsilon. \)
Ashwini Shirsat on 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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