You cannot understand calculus until you understand the Holy Grail of Calculus which is derived from my Historic Geometric Theorem of January 2020.
To understand the simplicity, elegance and genius of the Holy Grail of Calculus, follow the steps as outline:
Use Online Geogebra at: https://www.geogebra.org/classic
Step 1: Graph f(x)
Step 2: Place anchor point (x,f(x)) on graph of f(x)
Step 3: Draw tangent line at anchor point
Step 4: Place another point (x+h, f(x+h)) on f(x) to form a non-parallel secant line
Both points in step 2 and step 4 must be movable.
Step 5: Draw a horizontal through anchor point
Step 6: Draw a vertical through the other end point of the non-parallel secant line
Step 8: Intersect tangent line with vertical from step 6
Step 9: Intersect horizontal from step 5 with vertical from step 6
Join points of intersection to arrive at f1, f2 and h.
f'(x)= f2/h
Q(x,h)=f1/h
To test with other functions, simply change f(x). You may have to rescale axes to see all of the curve and diagram.
As a final exercise:
you can find the area under the graph of f'(x) from x to x+h by h[ f2/h + f1/h ].Be careful! The graph you are using is f(x), not f'(x). So the area will be for f'(x) and not f(x).
As a follow-up exercise, you can find the area under the graph of f'(x) from x to x+h by h*[ f2/h + f1/h ].Be careful! The graph you are using is f(x), not f'(x). So the area will be for f'(x) and not f(x).
You can check your answer by evaluating \int_a^b f'(x) dx because
\int_a^b f'(x) dx = h*[ f2/h + f1/h ]
Holy Grail (f(x+h)-f(x))/h = f'(x) + Q(x,h) described in detail here:
https://www.academia.edu/105576431/The_Holy_Grail_of_Calculus
and in far more detail with proofs here:
https://www.academia.edu/62358358/My_historic_geometric_theorem_of_January_2020
On Tuesday, 19 September 2023 at 10:22:44 UTC-4, sci.math wrote:
You cannot understand calculus until you understand the Holy Grail of Calculus which is derived from my Historic Geometric Theorem of January 2020.
To understand the simplicity, elegance and genius of the Holy Grail of Calculus, follow the steps as outline:
Use Online Geogebra at: https://www.geogebra.org/classic
Step 1: Graph f(x)
Step 2: Place anchor point (x,f(x)) on graph of f(x)
Step 3: Draw tangent line at anchor point
Step 4: Place another point (x+h, f(x+h)) on f(x) to form a non-parallel secant line
Both points in step 2 and step 4 must be movable.
Step 5: Draw a horizontal through anchor point
Step 6: Draw a vertical through the other end point of the non-parallel secant line
Step 8: Intersect tangent line with vertical from step 6
Step 9: Intersect horizontal from step 5 with vertical from step 6
Join points of intersection to arrive at f1, f2 and h.
f'(x)= f2/h
Q(x,h)=f1/h
To test with other functions, simply change f(x). You may have to rescale axes to see all of the curve and diagram.
As a final exercise:
you can find the area under the graph of f'(x) from x to x+h by h[ f2/h + f1/h ].Be careful! The graph you are using is f(x), not f'(x). So the area will be for f'(x) and not f(x).
As a follow-up exercise, you can find the area under the graph of f'(x) from x to x+h by h*[ f2/h + f1/h ].Be careful! The graph you are using is f(x), not f'(x). So the area will be for f'(x) and not f(x).
You can check your answer by evaluating \int_a^b f'(x) dx because
\int_a^b f'(x) dx = h*[ f2/h + f1/h ]
Holy Grail (f(x+h)-f(x))/h = f'(x) + Q(x,h) described in detail here:
https://www.academia.edu/105576431/The_Holy_Grail_of_Calculus
and in far more detail with proofs here:
https://www.academia.edu/62358358/My_historic_geometric_theorem_of_January_2020Calculus is 100% geometric. It DOES NOT require the BULLSHIT of infinity, infinitesimals or the circular rot of limit theory.
Newton, Leibniz and Cauchy were idiots who did NOT understand calculus and influenced the development thereof negatively.
I know better than you or anyone else! Don't believe me. Verify what I tell you because I and I alone, am RIGHT.
You cannot understand calculus until you understand the Holy Grail of Calculus which is derived from my Historic Geometric Theorem of January 2020.
To understand the simplicity, elegance and genius of the Holy Grail of Calculus, follow the steps as outline:
Use Online Geogebra at: https://www.geogebra.org/classic
Step 1: Graph f(x)
Step 2: Place anchor point (x,f(x)) on graph of f(x)
Step 3: Draw tangent line at anchor point
Step 4: Place another point (x+h, f(x+h)) on f(x) to form a non-parallel secant line
Both points in step 2 and step 4 must be movable.
Step 5: Draw a horizontal through anchor point
Step 6: Draw a vertical through the other end point of the non-parallel secant line
Step 8: Intersect tangent line with vertical from step 6
Step 9: Intersect horizontal from step 5 with vertical from step 6
Join points of intersection to arrive at f1, f2 and h.
f'(x)= f2/h
Q(x,h)=f1/h
To test with other functions, simply change f(x). You may have to rescale axes to see all of the curve and diagram.
As a final exercise:
you can find the area under the graph of f'(x) from x to x+h by h[ f2/h + f1/h ].Be careful! The graph you are using is f(x), not f'(x). So the area will be for f'(x) and not f(x).
As a follow-up exercise, you can find the area under the graph of f'(x) from x to x+h by h*[ f2/h + f1/h ].Be careful! The graph you are using is f(x), not f'(x). So the area will be for f'(x) and not f(x).
You can check your answer by evaluating \int_a^b f'(x) dx because
\int_a^b f'(x) dx = h*[ f2/h + f1/h ]
Holy Grail (f(x+h)-f(x))/h = f'(x) + Q(x,h) described in detail here:
https://www.academia.edu/105576431/The_Holy_Grail_of_Calculus
and in far more detail with proofs here:
https://www.academia.edu/62358358/My_historic_geometric_theorem_of_January_2020
Look f ckt rd, you really do not know much mathematics. Try learning it first before you can discuss it.
Look at this dude:
https://www.youtube.com/watch?v=63HpaUFEtXY
he knows mathematics.
On Tuesday, September 19, 2023 at 10:22:44 AM UTC-4, Eram semper recta wrote:
You cannot understand calculus until you understand the Holy Grail of Calculus which is derived from my Historic Geometric Theorem of January 2020.
To understand the simplicity, elegance and genius of the Holy Grail of Calculus, follow the steps as outline:
Use Online Geogebra at: https://www.geogebra.org/classic
Step 1: Graph f(x)
Step 2: Place anchor point (x,f(x)) on graph of f(x)
Step 3: Draw tangent line at anchor point
Step 4: Place another point (x+h, f(x+h)) on f(x) to form a non-parallel secant line
Both points in step 2 and step 4 must be movable.
Step 5: Draw a horizontal through anchor point
Step 6: Draw a vertical through the other end point of the non-parallel secant line
Step 8: Intersect tangent line with vertical from step 6
Step 9: Intersect horizontal from step 5 with vertical from step 6
Join points of intersection to arrive at f1, f2 and h.
f'(x)= f2/h
Q(x,h)=f1/h
To test with other functions, simply change f(x). You may have to rescale axes to see all of the curve and diagram.
As a final exercise:
you can find the area under the graph of f'(x) from x to x+h by h[ f2/h + f1/h ].Be careful! The graph you are using is f(x), not f'(x). So the area will be for f'(x) and not f(x).
As a follow-up exercise, you can find the area under the graph of f'(x) from x to x+h by h*[ f2/h + f1/h ].Be careful! The graph you are using is f(x), not f'(x). So the area will be for f'(x) and not f(x).
You can check your answer by evaluating \int_a^b f'(x) dx because
\int_a^b f'(x) dx = h*[ f2/h + f1/h ]
Holy Grail (f(x+h)-f(x))/h = f'(x) + Q(x,h) described in detail here:
https://www.academia.edu/105576431/The_Holy_Grail_of_Calculus
and in far more detail with proofs here:
https://www.academia.edu/62358358/My_historic_geometric_theorem_of_January_2020
You cannot understand calculus until you understand the Holy Grail of Calculus which is derived from my Historic Geometric Theorem of January 2020.
To understand the simplicity, elegance and genius of the Holy Grail of Calculus, follow the steps as outline:
Use Online Geogebra at: https://www.geogebra.org/classic
Step 1: Graph f(x)
Step 2: Place anchor point (x,f(x)) on graph of f(x)
Step 3: Draw tangent line at anchor point
Step 4: Place another point (x+h, f(x+h)) on f(x) to form a non-parallel secant line
Both points in step 2 and step 4 must be movable.
Step 5: Draw a horizontal through anchor point
Step 6: Draw a vertical through the other end point of the non-parallel secant line
Step 8: Intersect tangent line with vertical from step 6
Step 9: Intersect horizontal from step 5 with vertical from step 6
Join points of intersection to arrive at f1, f2 and h.
f'(x)= f2/h
Q(x,h)=f1/h
To test with other functions, simply change f(x). You may have to rescale axes to see all of the curve and diagram.
As a final exercise:
you can find the area under the graph of f'(x) from x to x+h by h[ f2/h + f1/h ].Be careful! The graph you are using is f(x), not f'(x). So the area will be for f'(x) and not f(x).
As a follow-up exercise, you can find the area under the graph of f'(x) from x to x+h by h*[ f2/h + f1/h ].Be careful! The graph you are using is f(x), not f'(x). So the area will be for f'(x) and not f(x).
You can check your answer by evaluating \int_a^b f'(x) dx because
\int_a^b f'(x) dx = h*[ f2/h + f1/h ]
Holy Grail (f(x+h)-f(x))/h = f'(x) + Q(x,h) described in detail here:
https://www.academia.edu/105576431/The_Holy_Grail_of_Calculus
and in far more detail with proofs here:
https://www.academia.edu/62358358/My_historic_geometric_theorem_of_January_2020
On Tuesday, 19 September 2023 at 13:12:27 UTC-4, Mathin3D wrote:
Look f ckt rd, you really do not know much mathematics. Try learning it first before you can discuss it.
Look at this dude:
https://www.youtube.com/watch?v=63HpaUFEtXY
he knows mathematics.
On Tuesday, September 19, 2023 at 10:22:44 AM UTC-4, Eram semper recta wrote:
You cannot understand calculus until you understand the Holy Grail of Calculus which is derived from my Historic Geometric Theorem of January 2020.
To understand the simplicity, elegance and genius of the Holy Grail of Calculus, follow the steps as outline:
Use Online Geogebra at: https://www.geogebra.org/classic
Step 1: Graph f(x)
Step 2: Place anchor point (x,f(x)) on graph of f(x)
Step 3: Draw tangent line at anchor point
Step 4: Place another point (x+h, f(x+h)) on f(x) to form a non-parallel secant line
Both points in step 2 and step 4 must be movable.
Step 5: Draw a horizontal through anchor point
Step 6: Draw a vertical through the other end point of the non-parallel secant line
Step 8: Intersect tangent line with vertical from step 6
Step 9: Intersect horizontal from step 5 with vertical from step 6
Join points of intersection to arrive at f1, f2 and h.
f'(x)= f2/h
Q(x,h)=f1/h
To test with other functions, simply change f(x). You may have to rescale axes to see all of the curve and diagram.
As a final exercise:
you can find the area under the graph of f'(x) from x to x+h by h[ f2/h + f1/h ].Be careful! The graph you are using is f(x), not f'(x). So the area will be for f'(x) and not f(x).
As a follow-up exercise, you can find the area under the graph of f'(x) from x to x+h by h*[ f2/h + f1/h ].Be careful! The graph you are using is f(x), not f'(x). So the area will be for f'(x) and not f(x).
You can check your answer by evaluating \int_a^b f'(x) dx because
\int_a^b f'(x) dx = h*[ f2/h + f1/h ]
Holy Grail (f(x+h)-f(x))/h = f'(x) + Q(x,h) described in detail here:
https://www.academia.edu/105576431/The_Holy_Grail_of_Calculus
and in far more detail with proofs here:
Hey moron.https://www.academia.edu/62358358/My_historic_geometric_theorem_of_January_2020
The OP clearly states that it's for human consumption, not fuckwads like you.
Impale yourself on a blunt pole, you fucking vile piece of shit!
FUCK OFF, MORON!
Is mathin3D being a bit of a flatface???????
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