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Post by P1kachu on Jun 2, 2015 12:56:03 GMT
*Requires the knowledge of algebra ( ͡° ÍÊ Í¡Â°)
Okay first of all, Calculus isn't that hard ( ͡° ÍÊ Í¡Â°)
But when you get to anti-differentation, that is where things get worse ( ͡° ÍÊ Í¡Â°)
What we will learn:
1. Limits
2. Differentation
3. Indefinite Integrals
4. Definite Integrals
Anyways,
LESSON 1: Limits I
Okay, so limits are just like substituting values for stuff.
For example:
lim x+1
xâ1
You read this as "The limit of x+1 as x approaches 1."
Now, to solve this equation. ( ͡° ÍÊ Í¡Â°)
All you have to do is to substitute x=1 into the equation, simple! ( ͡° ÍÊ Í¡Â°)
lim x+1 = (1) + 1 = 2
xâ1
Here is another question,
Now this is where things get crazy...
lim x/x
xâ0
When we substitute 0 for that, we get the indeterminate form, 0/0.
Therefore, you must "find a way" to make it substitutable (is that even a word lol ( ͡° ÍÊ Í¡Â°))
We can simplify x/x into 1 right? Therefore,
lim x/x = lim 1 = 1
xâ0aaalaaxâ0
Now this next one is tricky ( ͡° ÍÊ Í¡Â°)
lim x2+2x-3
xâ1aaax-1
All you need to do is to factorize x2+2x-3 into (x-1)(x+3) and divde it by x-1 afterwards, now we get:
lim x+3 = 4
xâ1
See? Calculus isn't that hard! ( ͡° ÍÊ Í¡Â°)
Well, more is coming soon, such as finding the limit of 1/x as x approaches 0. ( ͡° ÍÊ Í¡Â°)( ͡° ÍÊ Í¡Â°)( ͡° ÍÊ Í¡Â°)
I hope I made this clear for you guys... ( ͡° ͜ʖ ͡°)
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Post by Miguel888 on Jun 2, 2015 17:03:43 GMT
*Requires the knowledge of algebra ( ͡° ͜ʖ ͡°) Okay first of all, Calculus isn't that hard ( ͡° ͜ʖ ͡°) But when you get to anti-differentation, that is where things get worse ( ͡° ͜ʖ ͡°) What we will learn: 1. Limits 2. Differentation 3. Indefinite Integrals 4. Definite Integrals Anyways,
LESSON 1: Limits IOkay, so limits are just like substituting values for stuff. For example: lim x+1x→1 You read this as "The limit of x+1 as x approaches 1." Now, to solve this equation. ( ͡° ͜ʖ ͡°) All you have to do is to substitute x=1 into the equation, simple! ( ͡° ͜ʖ ͡°) lim x+1 = (1) + 1 = 2 x→1
Here is another question, Now this is where things get crazy... lim x/xx→0 When we substitute 0 for that, we get the indeterminate form, 0/0. Therefore, you must "find a way" to make it substitutable (is that even a word lol ( ͡° ͜ʖ ͡°)) We can simplify x/x into 1 right? Therefore, lim x/x = lim 1 = 1 x→0 aaalaax→0
Now this next one is tricky ( ͡° ͜ʖ ͡°) lim x2+2x-3x→1 aaax-1 All you need to do is to factorize x2+2x-3 into (x-1)(x+3) and divde it by x-1 afterwards, now we get: lim x+3 = 4 x→1 See? Calculus isn't that hard! ( ͡° ͜ʖ ͡°)
Well, more is coming soon, such as finding the limit of 1/x as x approaches 0. ( ͡° ͜ʖ ͡°)( ͡° ͜ʖ ͡°)( ͡° ͜ʖ ͡°) I hope I made this clear for you guys... ( ͡° ͜ʖ ͡°) It seems I dont need a tutor now lol. I can let you do my homework ( ͡° ͜ʖ ͡°) |
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Post by 《§》carbonara <3〖ƧƐ〗 on Jun 3, 2015 9:38:26 GMT
2easy4me ( ͡° ͜ʖ ͡°)
Should I make an introduction to Googology? <3
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Deleted
Deleted Member
Posts: 0
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Post by Deleted on Jun 3, 2015 10:04:03 GMT
*Requires the knowledge of algebra ( ͡° ͜ʖ ͡°) Okay first of all, Calculus isn't that hard ( ͡° ͜ʖ ͡°) But when you get to anti-differentation, that is where things get worse ( ͡° ͜ʖ ͡°) What we will learn: 1. Limits 2. Differentation 3. Indefinite Integrals 4. Definite Integrals Anyways,
LESSON 1: Limits IOkay, so limits are just like substituting values for stuff. For example: lim x+1x→1 You read this as "The limit of x+1 as x approaches 1." Now, to solve this equation. ( ͡° ͜ʖ ͡°) All you have to do is to substitute x=1 into the equation, simple! ( ͡° ͜ʖ ͡°) lim x+1 = (1) + 1 = 2 x→1
Here is another question, Now this is where things get crazy... lim x/xx→0 When we substitute 0 for that, we get the indeterminate form, 0/0. Therefore, you must "find a way" to make it substitutable (is that even a word lol ( ͡° ͜ʖ ͡°)) We can simplify x/x into 1 right? Therefore, lim x/x = lim 1 = 1 x→0 aaalaax→0
Now this next one is tricky ( ͡° ͜ʖ ͡°) lim x2+2x-3x→1 aaax-1 All you need to do is to factorize x2+2x-3 into (x-1)(x+3) and divde it by x-1 afterwards, now we get: lim x+3 = 4 x→1 See? Calculus isn't that hard! ( ͡° ͜ʖ ͡°)
Well, more is coming soon, such as finding the limit of 1/x as x approaches 0. ( ͡° ͜ʖ ͡°)( ͡° ͜ʖ ͡°)( ͡° ͜ʖ ͡°) I hope I made this clear for you guys... ( ͡° ͜ʖ ͡°) tl;dr |
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Post by [AT/DC] Peroxydisulfuric Acid on Jun 3, 2015 21:06:53 GMT
Why do things like this exist?
Also, Carboxylic Acid!
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Post by P1kachu on Jun 4, 2015 11:44:50 GMT
LESSON 2: Limits II
Okay, now let's look back at our question before:
lim x2+2x-3
x→1aa1x-1
When we try to graph the equation inside the limit, we get this:
As you can see, the graph looks really similar to y = x+3, except that it has a hole at point (1,4).
And as we can see, the answer to the limit is actually 4. Therefore, using graphs can help in solving limits.
Now let's try to solve this equation:
lim 1/x2
x→0
Graphing the equation y = 1/x2... (forgive my bad drawing skills pl0x ( ͡° ͜ʖ ͡°))
As we can see the graph, as x approaches 0, y continues to go up until infinity ( ͡° ͜ʖ ͡°)( ͡° ͜ʖ ͡°)( ͡° ͜ʖ ͡°)
lim 1/x2 = +∞
x→0
How about this one... Let sgn(x) be 1 when x is positive and -1 when x is negative.
lim sgn(x)
x→0
There are different limits depending on where x approaches from. So... yeah ( ͡° ͜ʖ ͡°)
We can see that when x approaches from the right, the limit is 1. We can write this as
limasgn(x) = 1
x→0+
That plus sign stand for "approaching from the right" ( ͡° ͜ʖ ͡°)
While on the other hand, approaching from the left gives -1.
limasgn(x) = -1
x→0-
You can probably guess what the minus sign stands for, rite? "approaches from the up", lol jk ( ͡° ͜ʖ ͡°)
Since the limits from approaching from left and right are different, there is no answer to the equation I given at first ( ͡° ͜ʖ ͡°)( ͡° ͜ʖ ͡°)( ͡° ͜ʖ ͡°)
Lastly, try to figure these ones out:
lima1/x
x→0+
Answer:+∞
lima1/x
x→0-
Answer:-∞
If you got all of these right, you are ready for infinite sequences ( ͡° ͜ʖ ͡°)
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Post by 《§》carbonara <3〖ƧƐ〗 on Jun 4, 2015 14:17:21 GMT
LESSON 2: Limits II
Okay, now let's look back at our question before:
lim x2+2x-3
x→1aa1x-1
When we try to graph the equation inside the limit, we get this:
As you can see, the graph looks really similar to y = x+3, except that it has a hole at point (1,4).
And as we can see, the answer to the limit is actually 4. Therefore, using graphs can help in solving limits.
Now let's try to solve this equation:
lim 1/x2
x→0
Graphing the equation y = 1/x2... (forgive my bad drawing skills pl0x ( ͡° ͜ʖ ͡°))
As we can see the graph, as x approaches 0, y continues to go up until infinity ( ͡° ͜ʖ ͡°)( ͡° ͜ʖ ͡°)( ͡° ͜ʖ ͡°)
lim 1/x2 = +∞
x→0
How about this one... Let sgn(x) be 1 when x is positive and -1 when x is negative.
lim sgn(x)
x→0
There are different limits depending on where x approaches from. So... yeah ( ͡° ͜ʖ ͡°)
We can see that when x approaches from the right, the limit is 1. We can write this as
limasgn(x) = 1
x→0+
That plus sign stand for "approaching from the right" ( ͡° ͜ʖ ͡°)
While on the other hand, approaching from the left gives -1.
limasgn(x) = -1
x→0-
You can probably guess what the minus sign stands for, rite? "approaches from the up", lol jk ( ͡° ͜ʖ ͡°)
Since the limits from approaching from left and right are different, there is no answer to the equation I given at first ( ͡° ͜ʖ ͡°)( ͡° ͜ʖ ͡°)( ͡° ͜ʖ ͡°)
Lastly, try to figure these ones out:
lima1/x
x→0+
Answer:+∞
lima1/x
x→0-
Answer:-∞
If you got all of these right, you are ready for infinite sequences ( ͡° ͜ʖ ͡°) will you talk of transfinites? ( ͡° ͜ʖ ͡°) |
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Post by [AT/DC] Peroxydisulfuric Acid on Jun 5, 2015 0:00:22 GMT
I don't like how that looks ;-; I don't want to leave 4th grade anymore ;~;
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Deleted
Deleted Member
Posts: 0
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Post by Deleted on Jun 19, 2015 18:21:34 GMT
This isn't calculus ( ͡° ͜ʖ ͡°)
Where are derivatives ( ͡° ͜ʖ ͡°)
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Post by 《§》carbonara <3〖ƧƐ〗 on Jun 19, 2015 19:12:11 GMT
This isn't calculus ( ͡° ͜ʖ ͡°) Where are derivatives ( ͡° ͜ʖ ͡°) derivates are a small part of Calculus, it has much more ( ͡° ͜ʖ ͡°) |
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Post by [AT/DC] Peroxydisulfuric Acid on Jul 14, 2015 3:47:36 GMT
Now I'm starting to notice how COSINE and Cyclics name are related to math  inb4 Geometry Dash becomes a math game oh god not again |
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![[AT/DC] Peroxydisulfuric Acid Avatar](http://41.media.tumblr.com/1e9155081c42b3e112d7c0c9bb6ab7ea/tumblr_inline_nzfg8aOPCr1rzvbv3_500.png)
