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I.S.I. and C.M.I. Entrance Corner

A familiar Functional Equation

Cauchy’s functional equations are very simple. The most familiar one has a simple formula: f(x + y) = f(x) + …

Contraction of a function – advanced Cheenta seminar

It is almost like deflating a balloon. But the effect is exponential.  Today (29th January 2018, Monday), we have a …

Graphing the exponential (TOMATO Objective 699)

Graphing an exponential function can be tricky. We are familiar with the graph of \( e^x \). But what if …

Graphing an Integral – Part 3

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Graphing an Integral – Part 2

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Graphing an Integral (B.Stat 2005 Problem 2)

In I.S.I.’s B.Stat Entrance 2005, the following problem appeared: Problem: Let $$ f(x) = \int_0^1 |t-x|t dt $$ for all …

Power Consumption of Electric Heater (KVPY ’10)

An electric heater coonsists of a nichrome coil and under \(220V\) consuming \(1KW\) power. Part of its coil burned out …

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