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Math 261-01 Exam 2 EC

Due: 12:30 pm on March 14th
Name : _____________________________________________________________________________
This optional assignment could up to 10 points extra credit to your Exam 2 grade. Please show appropriate work and use terminology and notation correctly. Unless specified otherwise, you should give exact answers. Partial credit will be given sparingly, if at all. Each problem is worth 1 point. Remember that these should help you practice some of the concepts you will be tested over, but this assignment should not be interpreted as a sample exam.
1. Find the curvature of the curve π‘Ÿπ‘Ÿβƒ—(𝑑𝑑)=<4sin(2𝑑𝑑),4cos(2𝑑𝑑),4𝑑𝑑>.
2. At what point on the curve π‘₯π‘₯=𝑑𝑑3,𝑦𝑦=5𝑑𝑑,𝑧𝑧=𝑑𝑑4 is the normal plane parallel to the plane 3π‘₯π‘₯+5π‘¦π‘¦βˆ’4𝑧𝑧=2?
3. Find the position vector of a particle that has the given acceleration and the given initial velocity and position:
π‘Žπ‘Žβƒ—(𝑑𝑑)=sin(2𝑑𝑑),𝑣𝑣⃗(0)=1,π‘Ÿπ‘Ÿβƒ—(0)=1
.
.
Name : ______________________________________________________________________
.. Page 2
4. (a) Evaluate the limit:
(b) Evaluate the limit: .
Name : ______________________________________________________________________
.. Page 3
5. Find for .𝑧𝑧=𝑦𝑦𝑦 𝑦 𝑦𝑦(6π‘₯π‘₯).
6. Find the equation of the tangent plane to the given surface at the specified point.
Name : ______________________________________________________________________
.. Page 4
7. Let and suppose that (x, y) changes from (2, –1) to (2.01, –0.98)
(a) Compute Ξ”z. (b) Compute dz.
8. Use the Chain Rule to find .
.
Name : ______________________________________________________________________
.. Page 5
9. Find the directional derivative of the function 𝑓𝑓(π‘₯π‘₯,𝑦𝑦)=(π‘₯π‘₯+6)𝑒𝑒𝑦𝑦at the point P(3, 0) in the direction of the unit vector that makes the angle πœƒπœƒ=πœ‹πœ‹3 with the positive x-axis.
10. Find and classify the relative extrema and saddle points of the function
𝑓𝑓(π‘₯π‘₯,𝑦𝑦)=π‘₯π‘₯2+2𝑦𝑦2+π‘₯π‘₯2𝑦𝑦+11

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