Monthly Archives: December 2025

An Interesting definite Integral for AP Calculus

Posted on December 16, 2025 by Sumant Sumant
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Zeroes of f'(x)

Posted on December 16, 2025 by Sumant Sumant
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Testing Convergence of Series using Integral test

Posted on December 16, 2025 by Sumant Sumant

What is the value of p for which

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Sum of digits from 1 to Billion

Posted on December 16, 2025 by Sumant Sumant

What is the sum of all the digits used in writing down the number from one to a billion

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Balls in the box

Posted on December 16, 2025 by Sumant Sumant

A manufacturer of steel ball shipped his 2” balls individually in a lined cubical box with inside dimensions of substantially 2” to ensure a snug fit. It occurred to him that he might use the space at the top four … Continue reading →

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Optimizing rectangle inside a ununiformly dialated circle

Posted on December 9, 2025 by Sumant Sumant

Find the maximal area of rectangle whose sides are parallel to the coordinate axes and whose vertices lie on the curve of equation

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Given the range of derivative values find the max and min value of a function at a particular point

Posted on December 9, 2025 by Sumant Sumant

If for all x in [1,4] and , find the maximal and minimal possible values of

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Replacing number by positive difference in first 2n numbers where n is odd.

Posted on December 9, 2025 by Sumant Sumant

Suppose the positive integer is odd. First AL writes the numbers 1,2,..,2n on the blackboard. Then he picks any two numbers a,b, erases them and writes, instead |a-b|. Prove that an odd number will remain at the end.

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If function f(x) achieves max at x=3 what happens to f^2(x) and e^(f(x)) at x=3

Posted on December 9, 2025 by Sumant Sumant

Suppose that a function f(x) has a maximum at x =3. True or False ? Justify a) The function has a maximum at 3. b) The function has a maximum at 3. c) The function has a maximum at 0.

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Fermat contest 2022 Problem 20 on telescoping series

Posted on December 5, 2025 by Sumant Sumant

A sequence of numbers has its terms defined by for every integer . For example . What is the largest positive integer for which the sum of the first terms (that is $latex t_1+t_2+\cdots+t_{k-1}+t_k) s less than 1.499?

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