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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 …

### B.Math 2005 Problem 5 Part 1

Problem Next Continue here

### 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 …

### Combinatorial Argument 2 – another problem from I.S.I. & C.M.I. Entrance

You may want to look into the first part

### 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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