# line

1. ### find equation of tangent line to graph at the function given value of x

f(x)= -2x^(1/2)+x^(3/2), x=4. So I know we need a point, and a slope. f(4)= -2(sqrt4) + (sqrt16) with an index of 3. f(4)= -4+ 2(sqrt2) with an index of 3. so are point is (4, -4+ 2(sqrt2) with an index of 3) now we need to find f'(4) to find the slope which is : limit of x approaching...
2. ### find all values of x where tangent line is horizontal

f(x)=2x^3+9x^2-60x+4 this polynomial is not factorable.. do I just put no x values as the answer or what should I put Woops.! My bad. I had to derive this whole equation with the power rule of derivative hehe :D
3. ### A line and a point not on the the line lies in one plane?

It is given that "a line and a point not on the the line lies in one plane." Why can't the point not on the line lie in another plane?
4. ### Rotation around a horizontal line..?

I'm not sure how to find the radius for this graph. I'm not even sure if I did the graph right. I read the radius is the actual function f(x) but also that the radius is the point plugged in to the function.. also that you are suppose to subtract the function from the line you are rotating...
5. ### line integral of scalar field

For line segment C3 , i think it's wrong ! It should be x = -2t +2 , y = 2t and z= -2t +2 , right ? Since the line c# move from (2,0,2) to (0,2,0) , at t = 0 , point = (2,0,2) , at t = 1 , point = (0,2,0) so , the line integral of C3 should be integrated from t = 0 to t = 1 , right ? if so , i...
6. ### Slope of a Straight Line

Hello, I am learning about the straight line and understand what the terms "rise" and "run" represent very well. I also understand how they are derived from the points positions in the plane. I really do not understand why the slope of a straight line is defined as "rise over run". How come is...
7. ### Least squared line of best fit - negative coefficient for y intercept

Hi I have a set of data that compares arm bone length (the predictor) with height (the response). I am having to read ahead due to deadlines so am hoping I have got this right. As I understand it the basic form of the least squared line of best fit is determined by (in its most general form)...
8. ### How to extend a line - is it even possible

Hi folks, Say you had two lines meeting to form an acute angle and you need to measure this angle. Normally you would just use a protractor or, for more accuracy, construct a right angle triangle from the two lines, measure OPPOSITE and ADJACENT and then refer to TAN tables. Say, in this...
9. ### line intergral of scalar field ( piecewise curve)

for the line segment c2 , why did the author want to differentiate dx with respect to dy ? and he gt dx = 0 ? I'm curious why did he didnt do so for C3 , where dy= 0 ..Why didnt he also differentiate dy with dx ? dy/dx = 0 ?
10. ### line integral

i'm not sure what is line integral... Does it mean total length of line under the curve?
11. ### line integral vs surface area integral

in part b , we can find mass by density x area ? is it because of the thin plate, so, the thickness of plate can be ignored?
12. ### finding line integral

for part b , the author sub x =t , i dont understand why he did so , can it be y = t or others? or , it must be x=t ? in the book , i was also told that i can use x = r costheta , and y = r sintheta for circular path ... I'm wondering can i use in this case ?
13. ### Chaikin's corner cutting Algorithm applied to a corner (two line segments)

Suppose I have two line segments A->B and B->C like in the image below. I offset both segments perpendicularly by distance "e" as shown by the blue lines. From the intersection point of the two lines, I draw the green angle bisectors that intersect my original line segments. The intersection of...
14. ### The Real Line Example Problem With Solution - Still Confused

Example 6 I'm confused as to how they got x<1, 1<x<3, 3<x<5, and X>5. I understand coming to the final answer and setting up a sign chart, but I have no idea how looking at the question and taking the three factors and coming up with the regions from only that bit of information. Please help...
15. ### What is the slope of the line according to the equation

Ok. I have been doing this all week long. However this problem has me stuck. Do I use the formula y = mx +b on this problem. I have a couple other problems like this, so if you could explain this problem on how you got what you did, I would appreciate it so I could do my other problems as well.
16. ### Distance from a point NOT on a line to the line

This problem has me a bit confused. I'm not totally sure if what I'm doing is right. My problem is with Steps 4 and 5. I'm not exactly sure what the problem means by asking what ||P0Q x u|| / ||u|| would look like. Based on the wording in Step 5 I assumed I was just supposed to write the...
17. ### Intersection between Bezier curve and Line segment

Hi, I'm trying to find the intersection between a Bezier curve and line. I have the parametric equation for a quadratic Bezier curve: X(t) = (1-t)^2X_0 + 2t(1-t)X_1 + t^2X_2\\ Y(t) = (1-t)^2Y_0 + 2t(1-t)Y_1 + t^2Y_2 I know the control points for the curve. I have the equation for a line...
18. ### Arc length of cardioid using line integral techniques

I've written out the question and my work thus far. If someone tell me if I'm on the right track or not, it would help a lot.
19. ### Proving a line is perpendicular to another line in terms of A,B,C...

Hi guys, I'm really stumped with question 1 of this assignment and was looking for some help. All input would be appreciated. Cheers. Sent from my SM-G900I using Tapatalk
20. ### Line Integral Problem

In (x,y,z) space, we are given the following vector field, $$V(x,y,z)=(\cos(y), -x\sin(y) + \sin(z), y\cos(z) + 2)$$ and the points $$O(0,0,0)$$, $$P(x_0, y_0, z_0)$$, $$Q(1,0,(π))$$ and $$R(-2,π,\frac{π}{2})$$ where $$(x_0, y_0, z_0)$$ are real numbers. (a) Determine the tangential...