# curves

1. ### Area Between Curves

I am trying to find the area bounded between the curves ln(x) and x-2. The ln(x) function is greater than the linear function between the two intersection points so this is a pretty straight forward area problem in terms of setting up the integration except for the limits of integration. I can...
2. ### Integral area calculation between 3 curves

Im suppose to calculate the area between y=x/3 , y=x+2 and y=x-2 My attempt is to firstly get the area over the x axis and then multiply it by two since it looks like its the same area under and over. \frac{A}{2}=\int_{-2}^{1}(x+2) dx +\int_{1}^{3}(\frac{3}{x}-(x-2))dx This looks right to me...
3. ### find the area of region enclsed by the curves

i am to ask to , given that x = 3(y^2)-5 , x = -(y^2) + 3 , y =x here's my working , the final ans given is 16.64 , but i only gt 0.716, which part of my working is wrong . P/s : firstly , i find the intersection point between the curves first ...
4. ### Shaded Region, Area between Curves and X-axis

Is there a formal way to approach finding the area of the shaded region in this diagram? From the examples it looks like they're flipping the sign of the entire integral. Both of them, actually. Btw, the answer is: \int_{-\sqrt{10}}^{-1}(-x^2+10)dx+\int_{-1}^{0}-9xdx
5. ### Area Between Curves

Hi, I have a question here that is asking for the area of two curves to be expressed in terms of one or more integrals with respect to x, and then the same for y. The two curves are y = 9x and y = x^2-10, and when I set them equal to each other and solve for x I get upper and lower bounds that...
6. ### Finding the area between two curves

"Find the area contained between the curves y=x^2-6x+4 and x+y=0" My question is: Is there a way to tell which graph is the outer/top curve and which would be the inner/lower curve without having to draw a graph?
7. ### level curves of the function

Find level curves of the function. Draw enough of them that you can form a picture of the function graph 1-f(x,y)=1/(x^2-y^2) 2-f(x,y) = e^(x^2-y^2) 3-f(x,y)=e^(x^2-y) 4-f(x,y)=x/(x^2+y^2)
8. ### level curves of the function

<br><span style="color: rgb(255, 255, 255); font-family: Roboto, arial, sans-serif; font-size: 20px; background-color: rgb(66, 133, 244);">Find level curves of the function. Draw enough of them that you can form a picture of the function graph<br><br>1-f(x,y) &nbsp;= 1/(x^2-y^2)<br>2-f(x,y)...
9. ### Intersecting and Colliding Curves

The particles don't collide because no value of t satisfies all three sets of parametric equations set equal to each other. Would the next step of seeing which points intersect involve solving the parametric equations for t?
10. ### Polar Curves

Do I need to convert the equation into rectangular form first? I'm not sure how to do that though using just the basic equations (x=rcostheta, y=rsintheta, x^2+y^2 = r^2)
11. ### Curves on a Plane

We are given the position of the particle at time t. (a) Find an equation in x and y whose graph is path of the particle. (b) Find the particle's velocity vector at the given value of t. (a) x^{2} - 2x - ?? (b) r(t) = (t + 1)i + (t^{2} - 1)j t = 1 v = (t)i + (2t)j, v(1) = (1)i +...
12. ### Real Algebraic Curves

I am reading C. G. Gibson's book: Elementary Geometry of Algebraic Curves. I need some help with aspects of Example 1.4 The relevant text from Gibson's book is as follows: Question 1 In the above text, Gibson writes the following: " ... ... Then a brief calculation verifies that any...
13. ### Affine Algebraic Curves - Kunz - Theorem 1.3

I am reading Ernst Kunz book, "Introduction to Plane Algebraic Curves" I need help with some aspects of Kunz' proof of Theorem 1.3 ... The relevant text from Kunz is as follows: In the above text we read the following: " ... ... Therefore let p > 0. Since a_p has only...
14. ### Affine Algebraic Curves - Kunz - Definition 1.1

I am reading Ernst Kunz book, "Introduction to Plane Algebraic Curves" I need help with some aspects of Kunz' Definition 1.1. The relevant text from Kunz' book is as follows: In the above text, Kunz writes the following: " ... ... If K_0 \subset K is a subring and \Gamma = \mathscr{V}...
15. ### Affine Algebraic Curves - Kunz - Exercise 1 - Chapter 1

I am reading Ernst Kunz book, "Introduction to Plane Algebraic Curves" I need help with Exercise 1, Chapter 1 ... Indeed ... I am a bit overwhelmed by this problem .. Exercise 1 reads as follows: Hope someone can help ... ... To give a feel for the context and notation I am providing...
16. ### how to draw level curves

im given f(x,y) = xy and i need to draw level curves for this have not any idea how can anyone explain to me in details the steps i need to take when im given these types of questions??
17. ### Curvature and solving a limit for planar curves

Hey guys, I've been stuck on this limit for a while. I tried representing the curve in a basis with the unit tangent and the principal normal. I didn't really know what to do from there.
18. ### Finding planar curves with constant curvature

Hey guys, I'm completely stuck on the following question: Find all planar curves with constant curvature When K = 0, it is simply a line. That is easily shown by equating r'(t) = r'(0) and integrating both sides. This is not applicable when curvature is non-zero.
19. ### curves, surfaces and tangent lines

Could someone please assist with the following questions: Consider $f(x,y) = x^{\frac{1}{3}}y^{\frac{1}{3}}$ and take $C$ to be the curve of intersection of $z = f(x,y)$ with the plane $y=x$. Show that the curve $C$ has a tangent line at the origin? I have tried showing that the directional...
20. ### gradient vectors and level curves

Hi, consider a function of two variables, $f(x,y)$. It is stated that at level curves (i.e. f(x,y) = k), it follows that $\nabla f(x,y)$ is perpendicular to $f(x,y) = k$ at every point $(x,y)$. Firstly, $\nabla f(x,y)$ is a vector, so does this mean that $\nabla f(x,y)$ is perpendicular to the...