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- So we won’t actually be using this in class until April, but might as well get you thinking this way: Assuming θ is in radians. sinθ = tanθ = θ as shown in the image above.
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- Another image about sinθ = tanθ = θ
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- Chapter 2 begins.
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- v bar is average velocity. just plain v represents instantaneous velocity.
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- Secant lines (green) slowly turn into a tangent line (red) as the ∆t gets smaller and smaller and smaller until it finally turns into dt. So the slope of secant lines (∆x / ∆t) represents average velocities. The slope of tangent lines (dx/dt) represents instantaneous velocity at the point at which the line “kisses” the curve.
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- Showing secant (v bar) vs. tangent (v)
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- overkill probably, but making the very important point again. You’re welcome.
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- The “trio” derivative (slope graph of x vs. t, in other words dx/dt) and second derivative (slope of the slope graph of x vs. t . . . or . . . dv/dt . . . or d²x/dt²)
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- A student shows an example of the trio.
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- Derivative (slope) of y = x³ is y = 3x² Power rule shown graphically.
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- Zero slopes and point of inflection (turning into a local minimum or maximum)
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- A student determined that the slope graph had the function dy/dx = (x-4)²-2 .
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- The problems from the class discussion. deaths per week , vs. deaths per week per week. Okay . . . you had to be there.
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- two equations for v bar.
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- Average acceleration vs. instantaneous acceleration.
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- 1st Orange is the derivative of the 2nd Orange. Ain’t Physics cool.
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- Part 1 of 4. Symbol proof of the power rule for a parabolic function.
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- Part 2 of 4: You will have to know this for the test.
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- Part 3 of 4
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- Part 4 of 4
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- A couple of derivative rules.
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- Tthe two scenarios where acceleration is negative. Don’t use the word deceleration. It’s not even in the Physics dictionary.
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- the two cases of negative acceleration on one graph.
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- This si from the homework. I think it is the last problem on 2.1 I need to see THIS KIND of work on your papers.
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- Power rule for second derivatives.
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- Quartet
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- x double dot; x triple dot
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- V vs. t with slope of secant being average acceleration (a bar) and slope of tangent being instantaneous acceleration (a).
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- A map of 1% of the universe. SEE VIDEO—> https://vimeo.com/64868713#
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- Formal fundamental definition in Calculus of the derivative.
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- Q35 (Part 1 of 2) — KNOW FOR TEST.
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- Q35 (part 2 of 2)
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- A cool modification of the trio
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- Q54 – Q56
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- P24
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- A problem from our discussion.
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- Q57 ; Q59
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- From Calculus supplement #27
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- From Calc Supp #28
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- Calc Supp #31
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- THIS ONE WILL BE ON THE TEST.
NHS AP Physics C 