I use multivariable calculus (double/triple integrals) to calculate the volume of the famous Steinmetz solid that is obtained by intersecting two cylinders. One could do it using single variables, but the multivariable approach is more systematic. Enjoy!…

Derivative of a heart curve by implicit differentiation. This is definitely one of my favorite curves in calculus and we will find dy/dx by using implicit differentiation. If you are taking calculus 1, then this is a good practice to master your derivative…

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This video is about the absolutely wonderful wobbly table theorem. A…

So you think you can take the derivative, handout here: https://blackpenredpen.com/calc1 Please subscribe and share my videos to help my channel grow! 😃 Comm...

In this video, I will show you how to take the derivative with chain rule twice! So you think you can take the derivative (Practice#1), handout here: https:/...

How to find the differential? This question is from Stewart Calculus 8th ed, Sect3.10#17 Please subscribe and share my videos to help my channel grow! 😃 Comm...

Approximating (1.998)^4 by using differential,
Details about dy vs delta y, https://youtu.be/2ooWs_8hzxQ

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In this video, I calculate the volume of the Steinmetz 3-solid obtained by intersecting three cylinders, using a symmetry argument and cylindrical coordinate...

I'm thinking of a three digit number where the number exactly equals the sum of the factorial of each digit. What is the number?

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Limit and continuity, limit of arctan(1/(x-4)) as x goes to 4, Checking both sides of a limit, Please subscribe and share my videos to help my channel grow! ...

Some limits represent derivative!

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In this video (my first video on blackpenredpen’s channel), I show how to calculate the limit as x goes to 2 of 3x + 5 using the epsilon-delta definition of a limit. Enjoy!

Intermediate Value Theorem, Bolzano’s theorem

This question is an exercise from Stewart Calculus textbook. Sect2.5 #53

We will discuss the difference between delta y and dy. Delta y is the difference between y-value value and the original y-value. But dy is the differential and it's an approximated difference between the y-values.
For more calculus tutorials, please check…

In this video, I give an actual definition of the half derivative and use it to calculate the half-derivative of x. Thankfully we get the same result.

In the next video, I use that definition to calculate the half-derivative of ln(x)

We prove that e is irrational by examining its series expansion and asking for a little bit of help from our friend Joseph Fourier.

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In this video, I calculate the limit as x goes to 3 of x^2, using the epsilon-delta definition of a limit.

speeding up or speeding down, rate of change of position Please subscribe for more calculus tutorials and share my videos to help my channel grow! 😃 Comment ...

derivative of ln(x) vs derivative of ln(abs(x))

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