Riemann sum limit. In fact, we will interpret this limit as an integral. We will see the indeterminate form of 0+0+0+... doesn't necessary approach 1. This is actually the integral of sqrt(x) from 0 to 1 and we get 2/3 for the answer. If you would like more…

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Make the equation correct by adding one blue dot, or erasing one blue dot. A single dot changes everything!

Keep It 💯 Puzzle: 4 dots to make this true!
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We will do the integral of sin(ln(x))/ln(x) from 0 to 1 by using Feynman's Trick (aka differentiation under the integral sign). This is also closely related to the Dirichlet Integral, which is the integral of sin(x)/x from 0 to inf.
For the complex exponential…

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Proof of L'Hopital's Rule (also spelled as L'Hospital's Rule) for the 0/0 indeterminate form.
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Thanks to Muztoba Ali in Bangladesh for this problem! Two brothers, A and B, have the exact same walking speed and the exact same running speed. One day they started the same trip to the same place. Brother A walked for half of the distance and ran the rest…

How to find the inflection points from the original graph, the derivative graph, and the second derivative graph? Enjoy! Please subscribe and share my videos...

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Catch James in a recent Objectivity video…