The feel

What is it about calculus that just makes it feel so different from learning any other math? The fact that there's a Calc 1-3 shows how much importance it holds. There's a different feeling I get when I'm 19 and have mastered differential Caclulus. There's something different about being skilled at calculus in this day and age.

you haven't mastered calculus until you get your master's in differentiation of e^x

calculus sucks compared to diffyqs and linear algebra

Calculus is very rote, very applied, and resultantly quite mundane. There's really not much to it. It's pretty intuitive and shallow (as it is taught in schools), and that's why people enjoy learning it. It is something that is perceived by others to be a lot more difficult than it actually is, thus boosting confidence and self esteem.

this right here. it was literally invented for engineers.

DE is even more autistic than Calc 1-3.

Think of it this way. Every single subject of level of math up to and including math is the English equivalent of vocab and grammar. Not till advanced math do you start actually exploring things on the level of novels as you would in english.

>Every single subject of level of math up to and including math is the English equivalent of vocab and grammar.

Fuck me

Every single subject of math up to and including calculus is the English equivalent of vocab and grammar.

Calculus is the first time in a usual conventional mathematical education, indeed even in a self-directed mathematical education, where it happens that the student and doer of mathematics must, or should, be juggling more like 3-5 differerent considerations, concepts, computations all at once in any given moment, as opposed to the one or two which are involved with doing the babby math of before. Also getting to play with the fancy symbols which are used in cute clip art (OP's pic related) also helps.

I'm not involved in this budding spat, but let me suggest that the other user is onto something insofar as a calculus education actually entails the /narrative/ of a proof (which is usually significantly more complex than anything that the student has ever seen before, and is the first thing that they've ever seen that rises to the level of a proper mathematical argument), and that even such proof-narratives entail retaining 3-5 abstract pieces of information, all at once. This is the challenge, the learning curve from babby into intermediate mathematics, which is exactly what the transition from precalc into calculus represents. And yes, calculus is so "intermediate mathematics", as I have said. If a simple majority of the human population struggles with the concepts, then this is a fair starting point for us to differentiate, pun not intended, between the tiers.

Very well put, as hoped to describe it in these posts.

>What is it about calculus that just makes it feel so different from learning any other math?

It isn't It's hyped up by people who think it's hard.
It's no harder than algebra and precalc, just a different focus. You're focusing on instantaneous rate of change instead of average rate of change.

Real math starts at analysis.

Describe analysis

It's the underlying, rigorous logic behind why Calculus "works." Except you're not really taught that in a step-by-step hand holding way, you're given the tools (a bunch of theorems) and mostly discover it yourself by proving shit and seeing how it works.

Applied sure, but rote? There is plenty of creativity in calculus (and by that I mean analysis, they are the same subject).

It is important for physics and other applied areas. But many other areas are important in physics too, calculus is like 17th century physics.

...

what a shitty drawing

Is that a vulva?

So its like Trignometry?

>poster in a math thread isn't quite exactly sure what a pussy looks like

comedy gold

Calculus "feels different" because
1) it's made up bullshit (cf. Wildberger)
2) it's probably the first time you ever solve interesting word problems which makes it marginally more exciting than algebra

Can someone please help me with this?

I don't understand what they want me to do with these trig identity problems.

>inb4 read it or talk to tutor
I tried, neither one work. Please help

man come the fuck on it's not even an indeterminate form

dude I'm terrible at math and the textbook is shit and the professor is never available to answer questions.

please help

>substitution
>l'hopitals

try those

can show me how to solve it and then I'll ask what parts I don't understand that you are doing?

try asking the following:
>classmates
>study centre
>tutor
>professor during office hours

>classmates
I posted to the discussion board, no answers
>study centre
don't have any
>tutor
don't have any
>professor during office hours
its an online class and she answers her emails once every 3 days

the class is past the add/drop date

I did not realize I would have these many problems and not be able to get an answer until after the add/drop date. now if I drop I will have a 'W' on my transcript.

seriously dude help me out, I'm trying to learn

Not him but what are you talking about?

When doing one sided limits are yout not supposed to just plug in values like 0.499999 into the function with your calculator and see what happens?

Maybe do some algebraic manipulation beforehand to make it simpler?

I mean, here all he needs to know is that sec of pi/2 is infinity and -infinity and all he has to do is check to which infinity it tends when you approach it from the left. This you can do with a calculator, by plugging x=0.499999...

I mean, this is how I did it back in Calc I. I only actually used limits techniques when it cames to finding limits themselves, when you want to apply theorems.

Here you just want to do elementary analysis of the function.

shh, you're not supposed to help

;_; pls i beg of you

There is an asymptote at pi/2 so its either neg. infinity or positive infinity. Read the fucking book.

what book are you talking about? my textbook sucks ass and this is calculus, not fucking trig.

how the fuck am I supposed to memorize all these asymptotes

where do I even find reference for this?

and what does the preceding 5 in front of sin(pi x) do to the asymptote?

Jesus christ fucking kill yourself, my god.

>mother hands him a new food on a plate
>WHAT AM I UPPOST TO DO WITH THIS MA PUT IT IN MY BUTT WHY DO YOu DO THIS TO ME ALL THE TIME YOU'RE SUCH A BITCH

dude I'm serious

where do I find reference for these asymptotes? not every sec or tan graph is the same, so how the hell am I supposed to know what it's asymptote is just by looking at the equation

I can't help it senpai

when it comes to math I'm /dumb/, I don't think there's anything I'm worse at than math

You're not supposed to memorize a bunch of asymptotes, holy fuck. All you need to know to answer the question is that cos(pi/2)=0

but WHERE ARE YOU GETTING THIS FROM

where are you getting cos(pi/2) = 0 ?

look,

>5x sec pi(x)

if I plug in 1/2

>5(1/2) sec pi(1/2)

gives me

>5/2 sec pi/2

so what do I do with the 5/2? and where are you getting cos from?

sec is 1/cos, that's the definition
I'll give to you it's not a very commonly used notation but it was probably given in your lesson.

ok man, I get that sec = 1/cos

so what am I supposed to do with the 5/2?

Somewhere in your lesson it's probably been explained that [finite number]/0 is indeterminate.

but how am I supposed to know that cos(pi/2)= 0?

I don't understand where you are getting this 0 from

Try to understand the unit circle.

so I have to memorize the entire unit circle just to answer this simple question?

can you help me with pic related?

>so I have to memorize the entire unit circle
What is it you're studying?

what do you mean? I'm taking a Calculus class because it's required for my degree.

I get A's in all my other material, it's just that math in particular is giving me an anal prolapse. And of course if I can't pass math, I can't finish my degree.

> mastered differential calculus

Too bad all the major applications lie in taking area's of regions and volume's of shapes

integral and DE are very rote

plug and chug 5200 different equations, with very little theory.

>change of coordinates

In advanced cases

Yeah but you need the calc 1-3 autism to do that. So it's double autism. It never stops.

This. It's the only math class I haven't enjoyed.

slippery slope of autism

pretty soon you'll start looking at peoples fingers when they try to point something out

>tfw bloody bitten fingers

>bitch
>bitch
>bitch
>more bitching

>looks at problem
>killthestupid.jpg

in the time that you faggots sit here calling me stupid, you could have just answered my questions so I understand what the fuck I'm doing

it's been 4 years since I've taken trig

It's already been answered.

so for any constant c

lim c * f(x) = c lim (f(x))

constants are just scalers so they're not gonna affect the asymptote.

how are you supposed to memorize them? learn the unit circle.

since sec is the reciprocal of cos, find the points where cosine = 0, that tells you the points where sec is undefined (aka an asymptote)

can't spell it out much more

the unit circle is the single most important thing in all of trig so yes you do need to memorize it

do it right the fuck now.

also

>this is calculus not trig
>implying they aren't heavily related

ok but I don't understand how I'm supposed to convert the unit circle back and forth between sin, cos, sec, tan, etc. Can you give me an example?

the ordered pairs are cos(theta), sin(theta)

at the top of the circle (90 degrees or pi/2) is the ordered pair (0,1)

that means cos(pi/2) = 0, and sin(pi/2) = 1

any point where cos = 0, sec will be undefined and that point will be an asymptote

wouldnt that just be ln(x) ?

no

no thats the inverse

this shit doesn't make any fucking sense..

why is it that at any point where cos = 0 that sec will be undefined?

I firmly believe Linear Algebra is the start of real math

>4 years since I've taken trig
>hardly needing trig for the problem

Your gonna need this bub

because sec is 1/cos
if cos = 0, then sec = 1/0 which is undefined

and for the record i'm giving a very babby explanation here so don't be short.

so if it's csc 4x then it's same 1/sin4x and then what do I do?

Okay, you realize the hypotenuse is 1, hence unit circle right? The sine function takes whatever angle the hypotenuse is from the positive x axis, and returns the magnitude of the radius going in the y direction (I.e it gives you the y coordinates of the hypotenuse). The cosine function is similar but gives you x. All other trig functions are built in these (so tan gives you the slope of the hypotenuse).

according to the unit circle, sin is 0 when the angle is 0 or pi

sin is defined as your y distance up or down

so, sin(4x) = 0 implies that 4x = 0 and 4x = pi

therefore the x values you are looking for are at 0 and pi/4

also please post more thiqq qtπ and ill help you with calculus for as long as you want

but how do you determine just from 1/sin4x that sin(4x) = 0? that's not what I'm understanding

kek.

I didn't determine that, I was specifically LOOKING for the asymptotes of csc(4x)

and the ASYMPTOTES of csc(4x) are where sin(4x) = 0, and this is BECAUSE youre trying to make the denominator 0

also please go to desmos.com and start graphing things to see how functions look.

I don't understand what you're saying. Can you rephrase it for me in retard language?

How do I "look" for the asymptotes of csc(4x) when I don't have a graph?

okay so
an asymtote is where the function is undefined.
this WILL HAPPEN if you find a point where a division by 0 has happened

you CANNOT divide by 0, so that is your first step in trying to "find" an asymtote.

How do we go about finding a point where
csc(4x) is undefined?

well, since csc(4x) is defined as

1/sin(4x)

does it not follow that these would occur when the denominator is 0?

so take the denomiator

sin(4x)

and set it equal to 0

and solve for x

that is the only way to find asymptotes.

Not him, but you do have a graph of it. If you don't, you should have the tools to make it.

I think you need to really hit the prerequisites of you want to seriously learn calculus. What happens to the sin function when you multiply the arguments by a constant? What even is csc(x)?

ok thanks, let me do some more problems and see if I have trouble still

we don't, they are just giving us these equations, no unit circle, no graphic calc, no trig identities

when you are doing your homework, you can always go to an online graphing calculator and enter in the function.

www.desmos.com

I know but it's not the homework I'm worried about, it's the exam. Prof already said, no unit circle, no trig identities, no graphing calc

i understand that, i'm not telling you to graph so that you memorize things.

it may actually give you deeper understanding on how the functions behave.

i mean just look at this shit

now you see them both side by side and might notice that the csc graph jumps up to infinite or negative infinity whenever the sin graph hits 0

...

>I'm a retarded biology major who can't picture reference angles right away and compute a simple fraction mentally, so I need to depend on stamp-collecting angles.

this lol

it always makes me cringe when i hear about a chart of sin/cos/tan values for common angles or using the unit circle

draw a goddamn 30-60-90/45-45-90 triangle and remember what the ratios are instead of trying to memorize some picture of a circle or a chart

guys we get it, you're autistic.

as if you can't use the unit circle as a tool to understand trig better as a whole :)

I apologize for saying "memorize," i'll change that to understand.

And I know it's the dumbest thing to say on this board, but i'm not bio, i'm 4th year CS.

In this context Calculus will mean the stuff they teach engineers which a robot could do because it's literally memorize this and that.

No engineers are autistic enough to bother about depth abd take analysis classes.

TOP KEK
O
P

K
E
K

>DUDE JUST MEMORIZE TRIANGLES INSTEAD OF UNDERSTANDING THE UNIT CIRCLE LMAO
You might be brain damaged.

did that guy ever solve the limit problem?

it's me here

here's what I'm confused about

when I'm given a limit problem like
>4 Cos x
and the limit x-> c
>c=pi/3
and I find pi/3 is equal to 1/2 per the unit circle, how come it's not 1/2 * 4 is the final answer, but rather just 1/2 is the final answer?

shit nevermind that was a bad example because 4pi/3 is equal to -1/2

I taught myself Trigonometry, Summation, and Fourier Series in the senior year of high school with Desmos. Do not underestimate this thing.

thats bizzare, I would have to see the problem as it was written out.

keep posting more if you want

this answer is wrong,

why?

delta x goes to zero so the limit is -4

the answer was 2x-6

how about this one?

6x is continuous, cos(x) is continuous, so there is none.