Finding the Tangent of a point on a curve (problem driving me crazy )

In summary, the conversation was about a problem that the speaker had attempted multiple times but was unable to find the correct answer. They were trying to find t in a given equation and were having trouble because substituting 0 for t would result in an undefined number. Another person joined the conversation and suggested that t=1 would be the correct value to use.
  • #1
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Homework Statement


I've done this problem about 5 times, several different ways following many different examples but I can't seem to find the right answer or even figure out how they got one of the answers (y answer is given)

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The Attempt at a Solution



r(t) = (1+4*sqrt(t), t5-t, t5+t)

s(t) = P0 + tv (P and v are vectors)
s(t) = r(0) + tr1(0)

r1(t) = (2/sqrt(t), 5t4-1, 5t4+1)
r1(0) = ?
and this is where i get stuck because trying to substitute 0 in x equation will give you an undefined number...so I'm doing something wrong obviously...please help!
 
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  • #2
You want to find t such that (x,y,z)=(5,0,2). That's t=1, right? Why do you say t=0?
 

1. What is the tangent of a point on a curve?

The tangent of a point on a curve is a straight line that touches the curve at that particular point and has the same slope as the curve at that point.

2. How do you find the tangent of a point on a curve?

To find the tangent of a point on a curve, you need to calculate the slope of the curve at that point. This can be done by finding the derivative of the curve at that point. The slope of the tangent will be equal to the derivative at that point.

3. What is the purpose of finding the tangent of a point on a curve?

Finding the tangent of a point on a curve is useful in understanding the behavior of the curve at that point. It can also help in finding the rate of change of the curve at that point, which is important in many applications such as physics and engineering.

4. Can the tangent of a point on a curve be negative?

Yes, the slope of the tangent can be negative. This means that the tangent line will be sloping downwards at that point on the curve.

5. Are there any special cases when finding the tangent of a point on a curve?

Yes, there are special cases when finding the tangent of a point on a curve. These include finding the tangent at the maximum or minimum point of a curve, or at a point where the curve has a vertical tangent.

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