Calculus Queries (1 Viewer)

Aplus

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Aerath said:
But it was like basic first principles. Like differentiating x^2 - 2x from first principles. It wasn't something like...... differentiating x-0.5.
Yeah, but I'd only use it if the question forceably said, "Use first principles..."
 

bored of sc

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Did you guys know the differentiation of the formula of the volume of a 3D shape gives the formula of its surface area?

E.g.
V = 4/3pir3
= volume of sphere
dV/dr = 4pir2
= surface area of sphere
 

Aerath

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bored of sc said:
Did you guys know the differentiation of the formula of the volume of a 3D shape gives the formula of its surface area?

E.g.
V = 4/3pir3
= volume of sphere
dV/dr = 4pir2
= surface area of sphere
Yes. :p
That's the first thing our teacher taught us when teaching us how to differentiate. :p
 

tommykins

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bored of sc said:
Did you guys know the differentiation of the formula of the volume of a 3D shape gives the formula of its surface area?

E.g.
V = 4/3pir3
= volume of sphere
dV/dr = 4pir2
= surface area of sphere
Welcome to the world of volumes (if you're planning to do 4unit).

tripped me out when i realised the circumference -> area -> volume of a circle/sphere were integrals.

2pir -> pir^2 -> [pir^3]/3
 

the-derivative

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Aerath said:
Yes. :p
That's the first thing our teacher taught us when teaching us how to differentiate. :p
Same here.
Some people were having an argument with our teacher about the relevance of calculus and how it relates to 'real maths' (those individuals have been dropped from accelerated- thought I'd mention that) and our teacher showed us that, and that shut those people up.

I found it quite interesting as well =]
 

12o9

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bored of sc said:
Did you guys know the differentiation of the formula of the volume of a 3D shape gives the formula of its surface area?

E.g.
V = 4/3pir3
= volume of sphere
dV/dr = 4pir2
= surface area of sphere
Whoa. That's rather hectic.
 

Iruka

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the-derivative said:
Same here.
Some people were having an argument with our teacher about the relevance of calculus and how it relates to 'real maths' (those individuals have been dropped from accelerated- thought I'd mention that) and our teacher showed us that, and that shut those people up.

I found it quite interesting as well =]
Real maths only begins with calculus!
 

bored of sc

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the-derivative said:
Exactly...
Applications of Calculus to the Physical World....
Rates of Change, Exponential Growth and Decay, Simple Harmonic Motion, Projectile Motion... all seem more useful to me than knowing the s.a. of a cylinder.
But remember the surface area of cylinder can be figured out through the differentiation of the volume of a cylinder.

V = pi.r2.h
dV/dr = 2.pi.r.h <---- Equals the rectangular part wrapping around shape.

Then just add on the circles that enclose the cylinder:
S.A = 2.pi.r2 + 2.pi.r.h.
 

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