Tag: calculus

L’Hopital’s Limit From A Phone Game

One of my recently graduated students was playing a phone riddle game that required an answer to this level: Turns out the solution to the game was just simply the word “answer” as the instruction was to simply enter that in. However, the integral and the limit shown there...
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No, You Don’t Need Quadratic Formula

On the MANSW Facebook page, a fellow teacher from another school threw this question to the brain’s trust. All the answers provided to the problem by others used the Quadratic Formula, but the Algebra from those solutions was not exactly clean. Personally, I don’t think getting the answer in...
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The Perfect View

I don’t remember where I got this question from (probably a textbook somewhere) but I remember it specifically for the different kind of way I went about solving it. Most people like to make a single variable the subject before differentiating, and this is usually the only way they...
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Special Integral: \(\int_0^\frac{\pi}{2}\ln(\sin x)\;dx\)

I remember when I was in Year 12, we were given this question on an integration worksheet that challenged my friend, Parth, and I so much so that we stayed back after school to use the large whiteboard to solve this problem even after all our friends had left...
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Things to Reconsider: The Integral of \(\frac{1}{x}\)

Absolute Absolutes? Consider the following integral: \[\int \frac{1}{x}\,dx = \log_e|x| + C\] When learning this integral, teachers often stress the need to include the absolute value signs. The reasoning behind this is often to do with the fact that the logarithm of a negative number is undefined. However, is...
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