The feel

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

>>8342012
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.

>>8342025
this right here. it was literally invented for engineers.

>>8342017
DE is even more autistic than Calc 1-3.

>>8342012
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.

>>8342040
>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.

>>8342012

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.

>>8342041

I'm not involved in this budding spat, but let me suggest that the other anon 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.

>>8342051
>>8342041
>>8342040

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

>>8342012
>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.

>>8342138
Describe analysis

>>8342182
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.

>>8342025
Applied sure, but rote? There is plenty of creativity in calculus (and by that I mean analysis, they are the same subject).

>>8342012
It is important for physics and other applied areas. But many other areas are important in physics too, calculus is like 17th century physics.

>>8342255
what a shitty drawing

>>8342255
Is that a vulva?

>>8342190
So its like Trignometry?

>>8342361

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

comedy gold

>>8342012
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

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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

>>8343070
man come the fuck on it's not even an indeterminate form

>>8343089
dude I'm terrible at math and the textbook is shit and the professor is never available to answer questions.

please help

>>8343101
>substitution
>l'hopitals

try those

>>8343116
can show me how to solve it and then I'll ask what parts I don't understand that you are doing?

>>8343120
try asking the following:
>classmates
>study centre
>tutor
>professor during office hours

>>8343132


>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

>>8343116
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.

>>8343155
shh, you're not supposed to help

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>>8343180

;_; pls i beg of you

>>8343070
There is an asymptote at pi/2 so its either neg. infinity or positive infinity. Read the fucking book.

>>8343208
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?

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>>8343215
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

>>8343227
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

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>>8343227
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

>>8343234
>>8343232
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

>>8343243
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?

>>8343249
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.

>>8343265

ok man, I get that sec = 1/cos

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

>>8343274
Somewhere in your lesson it's probably been explained that [finite number]/0 is indeterminate.

>>8343282
but how am I supposed to know that cos(pi/2)= 0?

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

>>8343292
Try to understand the unit circle.

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>>8343324
so I have to memorize the entire unit circle just to answer this simple question?

can you help me with pic related?

>>8343332
>so I have to memorize the entire unit circle
What is it you're studying?

>>8343342
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.

>>8342012

> mastered differential calculus

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

>>8342233
integral and DE are very rote

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

>>8343116
>change of coordinates

In advanced cases

>>8342032
Yeah but you need the calc 1-3 autism to do that. So it's double autism. It never stops.

>>8342032
This. It's the only math class I haven't enjoyed.

>>8343419
slippery slope of autism

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

>>8343423
>tfw bloody bitten fingers

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>>8343136
>bitch
>bitch
>bitch
>more bitching

>looks at problem
>>8343070
>killthestupid.jpg

>>8343436
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

>>8343441
It's already been answered.

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>>8343215
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

>>8343359
>>8343359
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

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>>8343447
>>8343451
>>8343457

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?

>>8343458
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

>>8342015
wouldnt that just be ln(x) ?

>>8343469
no

>>8343469
no thats the inverse

>>8343466
this shit doesn't make any fucking sense..

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

>>8342138
I firmly believe Linear Algebra is the start of real math

>>8343474
because sec is 1/cos
if cos = 0, then sec = 1/0 which is undefined

>>8343474
and for the record i'm giving a very babby explanation here so don't be short.

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>>8343480
so if it's csc 4x then it's same 1/sin4x and then what do I do?

>>8343458
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).

>>8343491
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

>>8343491
also please post more thiqq qtπ and ill help you with calculus for as long as you want

>>8343498
but how do you determine just from 1/sin4x that sin(4x) = 0? that's not what I'm understanding

>>8342015
kek.

>>8343502
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

>>8343505
also please go to desmos.com and start graphing things to see how functions look.

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>>8343505
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?

>>8343507
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.

>>8343507
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)?

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>>8343514
ok thanks, let me do some more problems and see if I have trouble still

>>8343519
we don't, they are just giving us these equations, no unit circle, no graphic calc, no trig identities

>>8343528
when you are doing your homework, you can always go to an online graphing calculator and enter in the function.

www.desmos.com

>>8343530
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

>>8343533
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.

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>>8343533
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

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>>8343457

>>8343457
>>8344037
>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.

>>8344196
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

>>8344196
>>8344665
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.

>>8342025

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.

>>8343475
TOP KEK
O
P

K
E
K

>>8344665
>DUDE JUST MEMORIZE TRIANGLES INSTEAD OF UNDERSTANDING THE UNIT CIRCLE LMAO
You might be brain damaged.

did that guy ever solve the limit problem?

>>8345151

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?

>>8345203
shit nevermind that was a bad example because 4pi/3 is equal to -1/2

>>8343539
I taught myself Trigonometry, Summation, and Fourier Series in the senior year of high school with Desmos. Do not underestimate this thing.

>>8345203
thats bizzare, I would have to see the problem as it was written out.

keep posting more if you want

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>>8345325
this answer is wrong,

why?

>>8345389
delta x goes to zero so the limit is -4

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>>8345416
the answer was 2x-6

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how about this one?

>>8345445
6x is continuous, cos(x) is continuous, so there is none.

>>8343458
HS senior here so I can explain the retard way.

Recall that [math]a^{2} + b^{2} = c^{2}[/math]
this is the Pythagorean theorem which essentially states that for every RIGHT triangle the squares of the smaller sides equal the square of the hypotenuse (the longest side.)

Now to relate this to a circle, let's recall that the definition of a circle is simply a shape in which all points are equidistant from the center.

Thus, the equation of a circle is just another distance formula, and distance formula is just another way to write the pythagorean theroem, this is because in a coordinate plane you can find the distance with two points by making the y axis a leg of a triangle and the x axis another and then find the the distance of the two points which should be the hypotenuse of that triangle you constructed.

Now the basic unit is 1, it's the multiplicative identity, it can generalize whatever model we construct to apply to other dimensions.

So a circle of radius 1, where cosine is the x value and sine is the y value would imply that [math]cos^{2} + sin^{2} = 1[/math]

So the unit circle is just a map of the different kinds of right triangles. The coordinates you'll find are (cosine,sine) like (x,y), the units are in radians.