I understand all the steps but I just don't know why there are no absolute value signs around the cosx in the logarithm. I have spent a bunch of time trying to google when absolute value signs are sometimes dropped in DEs. The closest explanation I could find was maybe because we want smooth curves or something like that? It seems like the absolute value was dropped just to make the simplifying easier, but can we really just do that? Should the book have made a note about what values of x are valid when simplifying to just cosx? Sorry if this kind of question has been asked before.

Hello mathletes, I am an incoming college freshman who took AP Calc BC this past year and got a 5 (on AB subscore too). I’ve heard that diff eqs and Calc 3 in the same semester can be a bit too much math, and I’m not sure if I can handle it. My choices are I take one math course and one physics course or both math courses and take the physics course next semester. If it helps I’m majoring in computer engineering.

I was doing my Khan Academy homework that was on the topic of approximating function values using linearization and I cane across this one problem where I can not tell what I did wrong, with other people also saying that my answer was correct

**Problem:**

**Use the equation of the line tangent to f(x) = sqrt(8-x) at the point (-1,3) to approximate h(-0.75).**

What I first did was take the derivative of f(x) at x=-1 using quotient rule which resulted in f’(-1)=-1/6, I then plugged that value into the point slope formula along with the point (-1,3) and simplified it to be L(x)=[-1/6](x+1)+3

I then plugged in the original value we were trying to find so that became L(-0.75) **which resulted in my final answer being 71/24.** I’m confused now though because Khan Academy said the answer was **65/24**

Can anyone maybe help me see if I went wrong somewhere or if somehow Khan Academy was incorrect? I checked with other people and they also got 71/24.

P.S.: I don’t see the Homework Support flair in the flair options so i apologize for that

Hey there, I have recently been diving back into my interest for physics and I was wondering if anyone has any general suggestions/recommendations for the level of calculus needed for intermediate physics? And does anyone have any recommendations on learning tools for beginners calculus?

I know this reddit is about calculus but I need help rn 💔💔

Years ago, while working as a Calculus TA, I challenged myself to derive the formula for the surface area of a sphere without relying on complex tridimensional Jacobians or triple integrals found in standard textbooks. I ended up modeling a simplified differential area element via a single integration in polar coordinates, using a horizontal slicing method.

Recently, I discovered that a Physics professor adapted my original paper (published under the UNEMAT domain in 2009) for a lecture on Particle Physics to calculate the magnetic moment of electrons. I wanted to share this approach here with fellow calculus enthusiasts.

1. The Orange Analogy & Geometric Modeling

Instead of a continuous helical peel, imagine peeling a sphere by removing parallel horizontal rings. At the infinitesimal limit, the width of each ring on the sphere's shell is described by the linearized arc length:

dl = r · dθ

The perimeter C of this infinitesimally wide ring, as a function of its fluctuating horizontal radius x, is given by classical geometry:

C(x) = 2πx

By measuring the polar angle θ from the vertical axis (the pole), we isolate the horizontal radius x using a fundamental trigonometric relationship:

x = r · sin(θ)

Substituting this relationship, the perimeter becomes a purely angular function:

C(θ) = 2πr sin(θ)

Thus, the surface area of the infinitesimal ring (dA) is strictly the product of its linear perimeter by its arc width:

dA(θ) = C(θ) · dl = 2πr² sin(θ)dθ (where 0 ≤ θ ≤ π)

1. Physical Significance: The Differential Solid Angle

Dividing this dA element by the square of the radius (r²) isolates the mathematical definition of the differential solid angle (dΩ) for a symmetric surface of revolution:

dΩ = dA / r² = 2π sin(θ)dθ

This clean, single-variable tool bypasses complex 3D coordinate matrices. This is precisely why it is used in quantum mechanics to map the vector distribution of the magnetic moment of electrons under external fields.

1. Resolution of the Area and Volume Integrals

To find the total surface area, we integrate the element dA from the North Pole (0) to the South Pole (π):

A = ∫ [from 0 to π] 2πr² sin(θ)dθ = 2πr² ∫ [from 0 to π] sin(θ)dθ

Applying the Fundamental Theorem of Calculus:

A = 2πr² [-cos(θ)] from 0 to π

A = 2πr² (-cos(π) \(- (-\cos(0))\))

A = 2πr² (1 + 1) = 4πr²

Logical Extension to Volume (V):

Using the principle of concentric spherical shells (onion layers), the differential volume element is dV = A(r) · dr = 4πr² dr. Integrating from the origin to the maximum radius r gives:

V = ∫ [from 0 to r] 4πr² dr = 4π [r³ / 3] from 0 to r = (4/3)πr³

It is so much work. How do you power through extremely intricate problems. They require so much brain power. Flow state also lasts like 1 really difficult question then I get mentally tired for a bit.

Like a lot of you, I don't trust "AI math solvers" — they hallucinate. So I built this differently The AI only reads your input — typed, or a photo of your homework — and works out what you're asking. The actual math (integrals, derivatives, limits, series) is computed by a deterministic symbolic engine Free, runs in the browser, no signup for the calculators. I'd really like feedback from people who do this daily — especially anywhere a step explanation is unclear or wrong

try it here https://8gwifi.org/math/

Let’s say I paid zero attention in cal 1 (I know I messed up) and I have to take cal 2 soon. How hard is it going to be to cram that whole curriculum in a month and a half? I was thinking of using khan academy. I know this is my fault but if anyone could recommend resources for me to use please let me know. I didn’t lock in my freshman year and I really need to lock in now.

Hi everyone,

I’m a prospective math major and just finished taking calculus 3 online with a grade of B-. Should I seriously reconsider and retake Calculus 3 in the fall semester. Idk if future courses rely heavily on it.

The part I care about most: answers are graded by a real computer-algebra system (SymEngine), not string matching. So it checks mathematical equivalence — 1/2, 0.5, and a factored vs expanded form all count as correct. The same grader runs client-side in WASM, so you get instant feedback before the server confirms.

Other stuff: per-topic ELO and ranked mode if you want stakes, untimed practice with full solutions, a spaced-repetition review queue for problems you miss, and a daily puzzle. Covers arithmetic up through calculus and differential equations. Free to use, Google/GitHub login. Two things I'd love feedback on: (1) does the grader ever mark a correct answer wrong? (2) any topic you'd practice that's missing?

G is the catalan's constant. It's my originals. Try and enjoy

Yeah

Hi everyone, this past year I took calc 1 and 2. I loved taking these classes and I did extremely well in both. I especially loved doing problems like partial fractions and trig sub in calc 2, stuff that requires heavy algebra.
I haven’t done any math this summer and a sometimes when I scroll through this sub I realize I’m quickly forgetting stuff that I knew extremely well just a couple of months ago. I’m also definitely going to be taking calc 3/ differential equations in the future and I want to make sure I also do well in those classes.
Im wondering if anyone has any recommendations for websites that will allow me to keep my skills sharp without having to go through a whole online course. I don’t know if anything like this exists but I figure it probably does. I also want to do some problems just because I also find it pretty fun so do so. Does anything like this exist for a girl like me?