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Based in the Seattle Area.

Free study guides and discussions about various topics in Mathematics. Thanks for stopping by!

My Math Teacher is Terrible! (I can help.)

Mar 2
Mar 2 A favorite Calculus resource: blackpenredpen!

Phil Petrocelli

Lots of good information is out there. Some people are really dedicated to their craft and to helping others. YouTube creator blackpenredpen is one such person.

Feb 26
Feb 26 L'Hôpital's Rule and Fundamental Theorem of Calculus (FTC) lurk!

Phil Petrocelli

Super interesting application of two useful techniques. Check this out!

Feb 24
Feb 24 Two ways to solve this (sort of) power-reduction Trig integral

Phil Petrocelli

Often, there are many ways to solve the same integration problem. This is an interesting one I saw on Reddit (r/Calculus) recently.

Feb 21
Feb 21 A tricky trigonometric integral with a surprising solution

Phil Petrocelli

This is one that shows that things play out in interesting ways, at times.

Feb 11
Feb 11 A challenging trig limit where L'Hôpital's Rule isn't so useful

Phil Petrocelli

When L'Hôpital's Rule isn't the savior that it usually is, slick algebra can help.

Feb 6
Feb 6 A L'Hôpital's Rule quickie!

Phil Petrocelli

Reddit (r/Calculus) provides, as does L’Hôpital’s Rule in the clutch!

Jan 31
Jan 31 A challenging L'Hôpital's Rule limit

Phil Petrocelli

Very interesting application of L'Hôpital's Rule, where we have a tough derivative that results in easing the situation.

Jan 24
Jan 24 A tough limit problem, two ways

Phil Petrocelli

This is one where we just have to crank through the solution. Fortunately, we have two techniques from which to choose.

Jan 17
Jan 17 An interesting u-substitution with a slight twist

Phil Petrocelli

Sometimes a problem is just nonstandard enough…

Dec 21
Dec 21 Converting a repeating decimal to a fraction

Phil Petrocelli

Repeating decimals are rational numbers. Rational numbers can be expressed as ratios of integers. Let's look at some techniques for moving easily between repeating decimals and their ratio forms.

Dec 12
Dec 12 Using the fraction features of the TI-84 family of calculators

Phil Petrocelli

Once we acquire a skill and practice it, learning new skills sometimes begs a few shortcuts around skills
we’ve already mastered. In particular, working with fractions - fractions with numbers, as opposed
to variables - is one such area. The TI-84 family of calculators provides a few timesaving features for
working with fractions.

Nov 16
Nov 16 A curve sketching question that hits all the finer points

Phil Petrocelli

How do I know that I understand the finer points of curve sketching using Calculus I techniques? If you can handle this one, you’ve got it.

Oct 26
Oct 26 A great use of implicit differentiation: easy slopes of tangents

Phil Petrocelli

We know that implicit differentiation helps in many situations where we are not able to easily separate the dependent variable from the independent variable (single-variable Calculus). This example problem reminds us of why this is so useful.

Oct 20
Oct 20 An implicit differentiation problem

Phil Petrocelli

Implicit differentiation is very useful in a number of tricky situations. Here, we'll use implicit differentiation twice to solve a tough problem, noting some important choices we make along the way.

Aug 30
Aug 30 Change this one thing about how you solve absolute value problems!

Phil Petrocelli

You were great at solving absolute value equations at one time, but now that you're working with absolute value inequalities, you can't get the right answer. Make the change!

Aug 10
Aug 10 Using trigonometric identities to solve an area problem

Phil Petrocelli

Applications of trigonometric identities are sup er useful in this triangle area problem.

Aug 2
Aug 2 An interesting similar triangles problem

Phil Petrocelli

Using a little insight, we can make a problem that looks to have difficult calculations a little easier.

Jul 19
Jul 19 When managing the path to solution is really important: A tricky 3rd derivative question

Phil Petrocelli

It took me several tries to get the differentiation correct! This is a tough one that demonstrates how keeping organized - somehow - can be an important part of problem solving.

Jun 22
Jun 22 Interesting exponents question with cool trick

Phil Petrocelli

A great example of how using a little bit of a trick avoids a whole lot of work. Nimble algebra is where it's at!

Jun 19
Jun 19 Rules of Exponents, Part 3: More advanced methods & finer points

Phil Petrocelli

Let’s tie everything together and check out all the rules in action as we make sense of our gibberish problem!

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