Recent content by madachi

c(t) = (cos(t) + C, sin(t) + K) t= 0, point is (0,0) So x(t) = 1 + C = 0, C = -1 And y(t) = 0 + K, K=0 So c(t) = (cos(t) -1 , sin(t) ) ?

Homework Statement Given that the tangent to the curve c(t) at any point on the curve is T(t) = (-sin(t), cos(t) ), find c(t) if the curve passes through the point (0,0) .The Attempt at a Solution I try to let c(t) = ( x(t), y(t) ) Then c'(t) = ( x'(t), y'(t) ) | c'(t) | =...

Thanks. How should we justify the answer though? I am not sure "what to say" to answer the question. Thanks.

Directed toward the axis. I have a question though, cos(At) and sin(At) aren't always positive, so does this still work? Thanks.

Away the z axis?

z = 1 ? I mean z is always equal to 1, unless you ask what z is for the normal, which is 0. I'm not sure about your second question, could you explain more? Thanks.

Homework Statement Let c(t) = ( cos(At), sin(At), 1) be a curve. (A is a constant) Show that the normal to c(t) is always directed toward the z-axis. The Attempt at a Solution I am not sure how to show this. (For example, is the question "asking" us to show the cross product of...

Homework Statement \int_{0}^{1} \int_{0}^{1} \sqrt{4x^2 + 4y^2 + 1} dx\,dy The Attempt at a Solution This integral is tough for me, I couldn't think of a way to evaluate it. Can you suggest me the first step to do this problem? Thanks!

Homework Statement Find the flow line curve c(t) to the vector field F = (x,-y) which passes through the point (1, 2) . The Attempt at a Solution So I let c(t) = (x(t), y(t)) . So c'(t) = ( \frac{dx}{dt} , \frac{dy}{dt} ) . Now, \frac{dx}{dt} = x and \frac{dy}{dt} = -y . So...

Homework Statement I am confused about spherical coordinates stuff. For example, we can parametrize a sphere of radius 3 by x = 3 sin \phi cos \theta y = 3 sin \phi sin \theta z = 3cos\phi where 0 \le \theta \le 2 \pi and 0 \le \phi \le \pi . I don't understand about the range...

Can line integral of a vector field ever be zero? If can, what is the interpretation of this value (0) ? Thanks.

I see, thanks!

I am confused. Could you show me the equation for one the curves so I can try to figure what you mean? Didn't I already show the equation of the 3 curves? Are they different from the ones that you just mentioned? Thanks.

The first two are parabolas. The last one is circle. So are the intersection points 1) (-2,0,0),(2,0,0) for the first curve. 2) (0,-2,0),(0,2,0) for the second curve. 3) (0,0,-4) for the third curve mentioned above? Thanks.

z = x^2 - 4 z = y^2 - 4 x^2 + y^2 = 4 Are these correct?