Sarah Mitchell

I keep seeing induction written as "base case, assume true for k, prove true for k+1", but I get lost in the actual algebra.

For example, how would I prove this without just memorizing the pattern?

I understand that factorial means multiplying down: $$5! = 5 \times 4 \times 3 \times 2 \times 1$$

My course plan is confusing me. Fourier series appear in differential equations, physics, signal processing, and sometimes after Calculus 3.

Do I need Calculus 3 before learning Fourier series, or can I learn Fourier with just Calculus 2 and some differential equations?

I understand basic ODEs like $$\frac{dy}{dt}=ky,$$

I just started Fourier series and every problem feels like a different trick.

I know the final answer usually looks like

I have a trig final next week and Im drowning in identities.

Theres like 50 of them:

• Pythagorean identities
• Angle addition formulas
• Double angle formulas
• Half angle formulas
• Sum-to-product
• Product-to-sum
• Power-reducing formulas

My friend told me that on multiple choice tests, you should always guess "C" if you dont know the answer because "C is the most common correct answer."

I said this is nonsense because test makers randomize correct answer positions.

I found this geometry problem on Twitter and nobody in my class can solve it: In triangle $ABC$, angle $A = 50^\circ$, angle $B = 60^\circ$, angle $C = 70^\circ$.

I had an exam question with a sin(2x) limit divided by x^3: $$\lim_{x \to 0} \frac{\sin(2x) - 2\sin x}{x^3}$$

I keep making this mistake on my calculus exams. When I see $f(x) = x^x$, my instinct is to use the power rule:

So theres this video going around showing a "Japanese multiplication method" where you draw lines for each digit and count intersections. For $12 \times 34$: 1 2 | | 3 ---|---|--- | | 4 ---|---|--- | |

I heard about Hilberts hotel. The one with infinitely many rooms thats always full but can always take more guests.

If the hotel is full and 1 more person shows up, each guest moves to room n+1 and room 1 is free.

ok i know this gets asked a LOT but i still dont GET it. $$0.\overline{9} = 1$$

Im a teacher and my students showed me something weird. If you type: $$6 \div 2(1+2)$$