**Unformatted text preview: **length of the curve γ ( t ) = ± e t , sin 2 t,t 2 ² 3 between t = 1 and t = 4. (10 points) 6. Use Gaussian elimination to completely solve the linear system 2 x 1-x 3 + x 4 = 1 x 1 + x 2-x 3 +2 x 4 = 0 2 x 2 + x 3-x 4 = 2 4 (10 points) 7. Use Gaussian elimination to ﬁnd the inverse of the matrix 3 0 1 0 1 0 1 1 0 5 (10 points) 8. Calculate the curvature κ of the curve g : R → R 3 given by g ( t ) = cos 2 t sin 2 t 2 t at the point g (0) = (1 , , 0). (10 points) 9. At the point (1 , 1), what is the direction of greatest increase of the function f ( x,y ) = x 2 + y 2 ? Give a rigorous mathematical explanation for your answer. 6 (10 points) 10. What is the equation of the tangent plane to the graph of f ( x,y ) = x 2-y 2 at the point (1 , 1 , 0)? 7...

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- Spring '14
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- Calculus, Derivative, Continuous function, Euclidean space