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Unformatted text preview: year-old grandmother, who can only negotiate a slope with a grade of twenty-Fve percent or less. Will she be able to start walking uphill with you, or will you have to abandon her to ensure your cucumber sandwiches do not get soggy? 3. [10 marks] Suppose a = (1 , 2 , 3) and h : R 3 R is a C 1 function such that h ( a ) = 3 and h ( a ) = (2 , 4 , 5) . Compute d dt p h ( t 3 , 3 t 2 1 , h ( t, 2 , t + t 2 + t 3 ) ) P when t = 1. 1 4. (a) [5 marks] Consider the set C R 3 which is the solution of the system of equations arctan( x ) + ( y + 1) 5 = ( z + 1) 3 x 4 cos( x ) + z 2 = 1 + ( x 3) y. Show that in a neighbourhood of the origin, y and z can be rep-resented as functions of x . (b) [5 marks] Find the line tangent to C at the origin. Give it as a subset of R 3 . 2...
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