Limit Definition of Derivative

Calculus students first learn the limit definition of derivatives. Using limits, we can define the slope of a tangent line to a function. And we find the slope by taking the ratio of the change in y values to the change in x values. Our intuition always tells us that if the change in x values is utterly small, we get a good approximation of the slope of the tangent line. That’s why we define the tangent line’s slope as the limit of the slope of secant lines as h approaches.

However, there is a better way to tell all those stuff in calculus; the derivative of f of x, f'(x). This math meme literally depicts calculus students when they realize they can use a simple notation for derivatives. Btw, if you want to learn calculus, you should check the online tool, Calculus Made Easy, or you can buy Spivak’s classic calculus book!

Cantor’s Breakfast

Georg Cantor's findings have played an important role in shaping modern-day mathematics in advancing further discussions on these topics. Artist Kevin Van Aelst took this beautiful photo and called it "Cantor's set."…

Snow Dodecahedron

Winter is here. Moreover, snow is a beautiful reason to spend some time with the kids. This snow dodecahedron is a perfect geometry project idea! In geometry, a dodecahedron is any polyhedron…

Why Does 0.999… = 1?

Interestingly, the real number 0.999 is actually equal to the integer 1. It may not make sense at the beginning for you, but there are many different proofs of the…

1/499999

Here is an interesting division 1/499999! If you divide 1 by 499999, you get all the powers of two up to six digits long.

37037037

37037037 is a pretty interesting number. When you multiply it with the multiples of 3, you get a beautiful pattern!

13177388

13177388 is a super interesting number. You can write with the sum of the powers of sevens, and 13177388 = 7¹+7³+7¹+7⁷+7⁷+7³+7⁸+7⁸.