Math

[GorgoBlesk 831]

Math + Tanki Online = Single Player :(

Math + War Thunder + Tanki + poems + drawing tanks and spaceships + chess = Forever Alone xD

[Guest]

FInally solved by myself

Felt like I did something wrong,but I just solved that for fun :D

Well done! I'm still working away on Integration, so I don't fully understand but one day soon I will.

[Person_Random 4,991]

Well done! I'm still working away on Integration, so I don't fully understand but one day soon I will.

I need to go to chapter 5 and 8 and then I might be able to solve something like that.  Chapter 5 is in a few days!

[Cruelty 476]

Smart people here

[Guest]

I am currently trying to learn integration by substitution and integration by parts. Any suggestions on how to make it smoother?

[Person_Random 4,991]

Yeah kind of. (for integration by substitution).  Find a pattern (what is raised to a power)

 

 

Directly from the textbook:

1. Choose a substitution u=g(x). (Usually it is best to choose the inner part of the function (e.g. g(x) from f(g(x)))

2. Compute du=g'(x) dx.

3. Rewrite the integral in terms of the variable u.

4. Find the resulting integral in terms of u.

5.Replace u with g(x) to obtain an antiderivative in terms of x.

6. Check your answer by differentiating.

 

 

Example: Find the integral of (8x²+1)²(16x) dx

u=g(x)=8x²+1

du=16x  and if you see the pattern then integrate in terms of u.

which means we get 1/3(8x²+1)³

Differentiation to check: 1/3*(3(8x²+1)²(16x))=(8x²+1)²(16x)

 

Also, I'd be very glad to learn integration by parts!

[Guest]

Yeah kind of. (for integration by substitution). Find a pattern (what is raised to a power)

 

 

Directly from the textbook:

1. Choose a substitution u=g(x). (Usually it is best to choose the inner part of the function (e.g. g(x) from f(g(x)))

2. Compute du=g'(x) dx.

3. Rewrite the integral in terms of the variable u.

4. Find the resulting integral in terms of u.

5.Replace u with g(x) to obtain an antiderivative in terms of x.

6. Check your answer by differentiating.

 

 

Example: Find the integral of (8x²+1)²(16x) dx

u=g(x)=8x²+1

du=16x and if you see the pattern then integrate in terms of u.

which means we get 1/3(8x²+1)³

Differentiation to check: 1/3*(3(8x²+1)²(16x))=(8x²+1)²(16x)

 

Also, I'd be very glad to learn integration by parts!

Nice! I find that u-substitution appears to be in a sense coverting an unfamiliar expression to one which is easily differentiable (the derrivative of cosx is -sinx)

 

I can't provide an exper level of explanation in regards to integration, so someone who knows better than I, please feel free to jumpm in. The derrivation (pun intended) of integration by parts is as such:

 

(Dy/dx)(F(x)G(x)) = F'(x)G(x) + F(x)G'(x)

 

By integrating either side (and some manipulations) you get (the int is just short for integral):

 

(Int)F'(x)G(x) =F(x)G(x) - (int)F(x)G'(x)

 

For example: integrate xcosx

 

==> (Int)xcosx =F(x)G(x) - (int)F(x)G'(x)

 

Once you have this, you must decide on the remainder of the functions. So, let me make the following statements:

 

G(x) = x

F(x) = sinx

G'(x) = 1

 

==> (Int)xcosx =xsin(x) - (int)sinx

 

Therefore I have that:

 

(Int)xcosx =xsin(x) + cosx

 

Hope this helps.

 

Edit: I know there is no dx at the end. I just wanted to make it easier to read, sorry about that!

[r_JK140 46]

is there any practical uses of calculus in real life?

[Guest]

is there any practical uses of calculus in real life?

Of course! If you are interested in maximizing profit and have an equation, taking the derrivative can be immensely helpful. Alternatively, if you have the equation of the height of the tide, takings its secons derrivative would allow you to know at roughly which point in time the tide would cease to increase and start to decrease If you are trying to determine the number of people in a mall, when you have the equation for the number of people at any given momement, integrating it can be very useful. You could argue that everything I mentioned can be done in simpler ways, but look at the beauty of it. Mathematics can describe patterns and trends in real life in ways inconceiveable wityout it, especially calculus. Needless to say, there are many more applications.

[AncientFire 1,894]

RIP me I cant even remember what the top half of a fraction is called, I remember the bottom is denominator. But can someone tell me the top one?  :unsure:

[Person_Random 4,991]

RIP me I cant even remember what the top half of a fraction is called, I remember the bottom is denominator. But can someone tell me the top one?  :unsure:

Numerator.

[AncientFire 1,894]

Numerator.

lol i feel so dumb

[Person_Random 4,991]

It's ok, the best of us have to make room for more concepts in the future.  Hopefully, they never ask about the numerator in a vocab quiz.

[Guest]

Out of curiosity, are the haversine, havercosine and other functions still used today? Or are they a thing of the past?

[u812ic 1,629]

This is for all you whizz kidzz. I have a simple math problem...this is not a troll. For some reason my brain is not juggling the numbers right. 

 

I have to travel 1 000 km. I have traveled 81% of that. How many more km do I need to go? I'm getting 190 km. Is that right?

[Person_Random 4,991]

Out of curiosity, are the haversine, havercosine and other functions still used today? Or are they a thing of the past?

Probably not... I don't see them mentioned in the index.  It probably doesn't appear in single variable calculus, but maybe in multi.  Idk...

[iFros 1,891]

This is for all you whizz kidzz. I have a simple math problem...this is not a troll. For some reason my brain is not juggling the numbers right. 

 

I have to travel 1 000 km. I have traveled 81% of that. How many more km do I need to go? I'm getting 190 km. Is that right?

Let's call x the rest of the distance we needed to reach 1000km, then x = (19% * 1000km)/ 100% which is x = 190 km. with 19% = 100% - 81%

Edited February 14, 2019 by iFrosTiger

[Guest]

Probably not... I don't see them mentioned in the index.  It probably doesn't appear in single variable calculus, but maybe in multi.  Idk...

I don't think it should appear in calculus so much right?

 

I thought it falls under trigonometry, specifically spherical trigonometry.

[Person_Random 4,991]

I don't think it should appear in calculus so much right?

 

I thought it falls under trigonometry, specifically spherical trigonometry.

true.  then i checked my trig/precalc textbook and there was no reference to haversine.  On a totally different note i learned trig sub and integration by parts because we had a tractrix problem that was unsolvable.

[Guest]

true.  then i checked my trig/precalc textbook and there was no reference to haversine.  On a totally different note i learned trig sub and integration by parts because we had a tractrix problem that was unsolvable.

Good for you!

 

Well I imagine not. After a little investigation I've discovered that functions like the haversine function get classified as 3D trigonometric functions, and they aren't really used much anymore. Or, for that matter they aren't taught either.

[Person_Random 4,991]

Good for you!

 

Well I imagine not. After a little investigation I've discovered that functions like the haversine function get classified as 3D trigonometric functions, and they aren't really used much anymore. Or, for that matter they aren't taught either.

well, we live in a system of where people re-learn the content each year and add on.  So I had to learn from that program for 4 years.  Pretty sure they would probably never use haversine.  Would take the nub teachers a year to learn themselves.

[snipe3000 678]

Algebra 2 anyone??   :D

Edited February 22, 2019 by snipe3000

[Fele5 27]

Can someone prove it why zero factorial equals one?

And how to calculate Euler's number? It equals 2.71828182845904523536028?74713527

Edited February 22, 2019 by Fele5

[Person_Random 4,991]

Can someone prove it why zero factorial equals one?

And how to calculate Euler's number? It equals 2.71828182845904523536028?74713527

1. Graph x! on your graphing utillity.

2. Use your calculator and press the e button.

 

 

Please keep in mind that these responses are highly sarcastic.

 

 

[Guest]

Can someone prove it why zero factorial equals one?

And how to calculate Euler's number? It equals 2.71828182845904523536028?74713527

Well I can't prove it, but zero factorial is defined as being one. This is so that 1 factorial can also be one (or so wikipedia said)

 

Euler's number can be considered to be the limit as x approaches positive infinity of the function (1 + (1/n))^n. Unfortunately, I can't prove that statement either, but if you go to a site such as Desmos and graph the same function (you'll have to use x instead of n) and observe what happens as you go up to millions or billions, you'll get an approximation of e (I think Desmos does 3 significant figures, so that'll be 2.718.