Calc 1 Definition and 73 Threads

I'm about to start calculus 1 at university. I have the course textbook in my native language, but I want to study it in english. Here's the table of content of the textbook after my translation attempt. do you know any good calculus textbook corresponds for this syllabus? thank you. have a nice...

my notebook says that we can rewrite the integral $$\int {75\sin^3⁡(x) \cos^2⁡(x)dx}$$ as $$\int {75 \cos^2(x)\sin(x)dx} - \int {75\sin(x)\cos^4(x)dx}$$ however, i have literally no idea how it got to this point, and i unfortunately can't really provide an "attempt at a solution" for this...

I'm trying to review some high school maths and work my way to Calculus and Linear Algebra, and I found these three translations of Japanese maths textbooks translated by the AMS and edited by Kunihiko Kodaira. The AMS links to them are: https://bookstore.ams.org/cdn-1669378252560/mawrld-8/...

Attached here is the full problem I am doing. I went through the problem and got my final answer which I thought was correct. Here is my work. They tell me I am wrong. Not sure where is the mistake.

dv/dt(mv^2-mv0^2) = dv/dt(kx0^2-kx^2)

As you can see form my previous posts, I am in my first university level calculus class ever. It is going very well, and through the class I am asking good questions and trying to actually make connection with the stuff we arr doing - not just doing the math just for the sake of passing - I am...

I am currently a community college student majoring in Computer Science, and I was placed into Calculus 1. I had to withdraw from this course for two semesters now. My professor advised me that I have "Algebra Issues". With my weaker foundation of Algebra, I plan to take the College Algebra...

I have seen two approaches to the method of integration by substitution (in two different books). On searching the internet i came to know that Approach I is known as the method of integration by direct substitution whereas Approach II is known as the method of integration by indirect...

Homework Statement Force of jet= A(r(t))4/3 A: constant determined by the fighter model in the class being considered and the drag force on the plane r(t): the rate of fuel consumption as a function of time Consider 3 possible situations for r(t): 1. when the rate is constant for the...

Homework Statement Homework Equations Stokes Theorem The Attempt at a Solution I'm having a tough time "cancelling" out integrals from both sides of an equation (if possible). On the right hand of the equation, we know since it is a closed curve, that Stoke's Theorem applies and we can...

Homework Statement Find the point "c" that satisfies the Mean Value Theorem For Derivatives for the function ## f(x) = \frac {x-1} {x+1}## on the interval [4,5]. Answer - c = 4.48 Homework Equations ##x = \frac {-b \pm \sqrt{b^2 -4ac}} {2a}## ##f'(c) = \frac { f(b) - f(a)} {b-a}## The Attempt...

Homework Statement Find critical numbers of the function: F(x)=t^3/4 - 2t^1/4 Derivative I got: F'(x)=3/4 t^-1/4 - 1/2 t^-3/4 Homework EquationsThe Attempt at a Solution I have found the derivative and I understand I must pull out a t in order to find critical numbers, and run across this...

Homework Statement Homework Equations d/dx The Attempt at a Solution d/dx (T) = d/dx(1/2mx'2) = mx'' d/dx(U) = d/dx(1/2kx2) = kx' ≠ kx It's probably me who made an error because I know that that equation (2.3) is the one I should be getting, but I don't understand how they did it because...

Homework Statement A coat of paint of thickness 0.02 in is applied to the faces of a cube whose edge is 10 in, thereby producing a slightly larger cube. Use differentials to find approximately the number of cubic inches of paint used. Also find the exact amount used by computing volumes before...

I'm going to have a gap between math classes at some point. I can either take calc 1, then calc 2 the following semester, then have a semester gap with no math, and then calc 3. Or calc 1, no math gap, calc 2, calc 3. The reason I am asking is because i will forget some information in the...

Homework Statement At time t, the position of a body moving along the s-axis is s= t^3 -12t^2 + 36t m(meters) Find the total distance traveled by the body from t = 0 to t = 3. Homework Equations Derivatives The Attempt at a Solution I got the derivative which is 3t^2 - 24t + 36(meters) I...

Mod note: Moved from technical math section, so there's no template. Sorry if I'm formatting this question wrong, new user. F(x) is an antiderivative of https://upload.wikimedia.org/math/9/1/5/915ca58b070b0328cd069524c2d487f2.pngx3+x+1...

I was given the equation of a polynomial told to find the derivative. easy enough. Then asked to give the equation of the tangent line which I've only learned how to get in the form of the question: "find the equation of the tangent line at x=" They gave me the equation of a line parallel to...

A charge Q is placed at a distance a = 3m and a charge q is placed at a distance b For what value(s) of b is the x-component of the force maximized? I know to maximize the force we need to maximize F_Qq = k Qq b/(3^2 + b^2)^{3/2}. To do this we need to set the first derivative to zero and...

I noticed the scan was cut off on the second image at the bottom right, but I came up with x= 31/5 My first test in Calc I begins tomorrow and I want to know that I'm headed in the right direction. I think I understand to some extent how logarithms can be expanded and condensed though I'm...

Got a bit of a long and nutty question here. So I got a nutty question from my Calc 1 class and was wondering if anyone could help me out A section of road, represented by the line y = x + 4 when x ≤0, is to be smoothly connected to another section of road, represented by y = 4 –x when x ≥4...

1. Evaluate the limit http://www4a.wolframalpha.com/Calculate/MSP/MSP64511d2754i3f4iaefab00001fa62g875680a1ia?MSPStoreType=image/gif&s=44&w=125.&h=45. 2. No formulas 3.The answer is -1/9. I have tried multiplying the top by the conjugate but that seems wrong as there are no square roots...

I'm attempting to help a tutoring student with this problem and I'm having trouble figuring out how to do it. 1. Homework Statement A marathon runner likes to practice by running in a large park that has a perfectly circular trail, with circumference 50 kilometers. She runs at a constant...

Homework Statement Use the intermediate value theorem and rolles theorem to prove that the equation has exactly one real solution 2x-2-cos(x)=0 The Attempt at a Solution Let the interval be [a,b] and let f(a)<0 and f(b)>0 Then by the IVT there must be at least one zero between a and b...

After taking an astronomy course in college, I decided I want to major in physics with a concentration in astronomy. My current major has nothing to do with science or mathematics. This summer I took a physics class and I'm currently still taking Calc 1. I got an A in physics, but so far in...

$$\int \sqrt{f(x)}dx$$ is NOT the same as.. $$\sqrt{\int f(x)dx}$$ right? i did an example problem and they turned out not to be equivalent but i just wanted to make certain. if they actually aren't equivalent.. why aren't they?

So I am attending Northeastern University as a Physics major and this fall will be my first semester. This year in high school I took AP Calculus AB, AP Chem, and physics honors. Unfortunately a month and a half before the AP exams I had a family issue that required me to miss A LOT of class...

If I understand my next possibilities in college, I think I can take either calculus 1 or trig 1, which do I take?

Find the value(s) of k such that f(x) is continuous everywhere: x^2-7 if x <= 2 and 4x^3-3kx+2 if x>2 Can you set the two equations equal to each other if only one of them has k in it?

[Mentor's note: This post does not contain the template for thread-starting posts in the homework forums, because it was moved from another forum.] "If f'(x) gives me the slope of f at some point, why doesn't f'(x)x + b = f(x)?" I have no idea how to answer this. Can you? How about: it is the...

Homework Statement Find (f−1)'(a). f(x) = 5x^3 + 3x^2 + 5^x + 4, a = 4 Homework Equations I'm not entirely sure but I assume I have to use d/dx(f-1) = 1/f '(f-1(x)) The Attempt at a Solution So far I switched y and x. Found dx/dy to be 15y^2 + 6y + 5. Then I switched dx/dy to...

Homework Statement Hey I'm doing something really stupid it is really pissing me off why I can't figure it out. The Attempt at a Solution Evaulate the integral : ∫ x(1-x)^1/2 I tried with substitution. u = 1-x , -du = dx and x = 1-u ∫ (1-u)(u)^1/2 I just tried to...

Homework Statement Use the The Fundamental Theorm of Calculus to Find the following answers f(x) = 0 IF x < -4 2 IF -4<=x<0 -3 IF 0<=x<5 0 IF x>= 5 g(x) = Integral of f(t) dt Between 4 and x Determine the value of each of the following: (a) g(−6)=...

I will be starting calculus 1 in a few weeks and I was wondering if i should use "Essential Calculus - Early Transcendentals" our reccomended textbook. I was going to buy it on amazon but noticed it got a lot of negative reviews. I am the sort of student that needs to learn a lot from the book...

Instead of making many threads on different questions, I have decided to make one thread and ask a variety of questions here instead. Homework Statement Suppose that g(x)= x+4/x+3 Write an equality about lim x\rightarrow-3^+ g(t) What is an equality? Is it possible to write an equality...

Hello everyone, I am currently using khan academy to teach my self trig and refreshing my memory on some algebra things I have forgot since I haven't taken a math course in 3 years. (algebra 2 was the last course). I have almost finished all the practice on khan with trig and am now ready for...

I got a B+ in calc 1! So I am new to this forum. First post! As you all can tell from my title I got a B+ in calc 1. I am declared as an EE major now, and was wondering how that grade stacks up. I was hoping for a A of course but didnt have the BEST study habits and because of that have an...

My math calc 1 class starts just 10 minutes after my physics class ends and it's on the opposite side of campus and yesterday I had my first exam in physics and ended up missing the first 3 minutes of my math class lecture. I copied the notes from the board, but didn't hear what he was saying...

Here is the situation: I'm a junior taking Precalc right now and I hope to take AP Calc BC next year. My guidance counselor told me that the AP Calc BC curriculum at our school is laid out so that it picks up right after where Calc AB lefts off, so AP Calc AB is an absolute prereq to take BC at...

I need to find an online Calculus 1 course. I am degree seeking, but I can enroll in the school offering the course as a student for their institution. I intend to pay cash for the class to forget the financial aid non-sense. I looked at www.distancecalculus.com and the RODP of tennessee. I...

Okay so the question involves finding the dimensions of a container of least cost given a specified volume and the cost of material on various surfaces. However it gets down to this one part where I have a number 2250. In my notes, my teacher automatically converts 2250 to (15^2)(10) as a...

Homework Statement Hey, I'm revising my calculus 1 test, I'm just not sure if this is a valid way to prove this. If f is continuous on [a,b] and if f'(x)=0 for every x in (a,b), prove that f(x)=k for some real number kHomework Equations Rolle's theorem: if f(a)=f(b), then there is some...

Homework Statement suppose f: [a,b] ---> Q is continuous on [a,b]. prove that f is constant on [a,b]. Homework Equations The Attempt at a Solution Since there is at least one irrational number between every two rational numbers, then for f to be continuous in the given scenario...

Homework Statement part 1)Show the function a(x)=|x| is a continuous function from R to R; part 2) Prove that if the functions f: D--> R is continuous at x=a, then l f l (absolute value of f) is also continuous at x=a. Homework Equations The Attempt at a Solution part 1)...

Hello, I am planning on majoring in physics in college next year. My school does not offer AP classes, and no Calculus at all. Will not taking Calculus in high school set me back for the first semester of undergrad? I have the option of taking it this summer, and I'm confident I can do well...

My major is chemical engineering. (I feel more like just a wannabe at this point, not an actual chemE student.) I'm really discouraged right now as I am questioning my suitability for the major/field. Basically I for the first two months of the semester I was working a lot. (32+ hours per...

Homework Statement f(x) = (x) / (x + (c/x) ) Homework Equations Product rule and quotient rule The Attempt at a Solution f'(x) = [ (x + (c/x)) - (x(1-(c/x^2)) ] / [ (s + (c/x)^2) ] = [x + (c/x) - x + (c/x)] / [(x+(c/x)^2)] = [2c/x] / [(x + (c/x)^2)] That's where...

So i went to my first calc 2 class today, and i was lost =( i took calc 1 2 semesters ago and i don't remember anything (i got a B+ on calc 1) few students felt the same way, and ask the professor what to do, and his reply was "will you consider take calc1 again? Thats my best advise" But i...

Hello all, I am heading back to school after 8 years to complete some Pre-Req course that will allow me to get into a Master's program. I have taken Pre-Calc over the summer and received an A. Is Physics 1 eaiser or harder, when you take Calc 1 concurrently? Thanks for any insight, Ernest G

Hey I am transfering to the University of Florida next semester. Which one of these classes is easier? Business Statistics or Calc 1 w/ analytical geometry? I want to go higher up in Math and I was thinking calc 1 w/ analytical might help me before I take Business Statistics? Right now I am...