  # v(t)= (4t^2, 2t^3-4t)that is x(t) = 4t^2 and y(t)=2t^2-4tfind formula for tangent line at t=1.  also generalize formula so that it works for any t.  What formula gives the length of this graph if t is less than or equal to 1 and greater than or equal to -1.  If it cannot be done, how do you estimate?

Question

v(t)= (4t^2, 2t^3-4t)

that is x(t) = 4t^2 and y(t)=2t^2-4t

find formula for tangent line at t=1.  also generalize formula so that it works for any t.

What formula gives the length of this graph if t is less than or equal to 1 and greater than or equal to -1.  If it cannot be done, how do you estimate?

check_circleExpert Solution
Step 1

To study the curve defined parametrically with parameter t.

Step 2

To find the slope at any t, calculate dy/dx at the corresponding value t.

Step 3

Fint the equation of the tangent line at t=1 ,using the slope calculation a...

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