Vector Function Help: Find F(t), Tangent Line, Point on Curve

mercedesbenz
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please help me, I try to do but i can not.

1. Find a vector function F(t) whose graph is the curve of intersection of
z=\sqrt{4-x^2-y^2} and y=x^2.

2. Find parametric equations for the line that is tangent to the curve r(t)=(e^t)i+(sin t)j+\ln(1-t)k at t=0.

3. Find the point on the curve r(t)=(12sin t)i-(12cos t)j+(5t)k
at a distance 13\pi units along the curve from the origin in the direction opposite to the direction of increasing arc length.
 
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I'm glad to hear you tried. Please show WHAT you tried so we can we will know what suggestions will help you.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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