1.Let y=6x^2. Find a parametrization of the osculating circle at the point x=4.
2. Find the vector OQ−→− to the center of the osculating circle, and its radius R at the point indicated. r⃗ (t)=<2t−sin(t), 1−cos(t)>,t=π
3. Find the unit normal vector N⃗ (t) of r⃗ (t)=<10t^2, 2t^3> at t=1.
4. Find the normal vector to r⃗ (t)=<3⋅t,3⋅cos(t)> at t=π4.
5. Evaluate the curvature of r⃗ (t)=<3−12t, e^(2t−24), 24t−t2> at the point t=12.
6. Calculate the curvature function for r⃗ (t)=<7, e^1t, 10t>.
7. Let r⃗ (t)=<11cost, 11sint> Find a parametrization of the osculating circle at the point t=π2.
According to rules and regulations, we are allow to do only one question at a time.. i provide you 2 solution..question 5 and 6
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