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midrev2 - t = 1(5 Find the limit or show that it does not...

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MAC 2313 SECTION 3117 REVIEW FOR MIDTERM 2 (A) The test will be closed-book and no graphic calculators will be allowed. You can bring a formula sheet (one page, letter size). (B) The test will consist of six word problems. No true/false questions will be given. (C) The following problems are desgined to illustrate what to expect on the test: (1) Find the length of the curve r ( t ) = (2 t,t 2 , ln t ) for 1 t e 2 . (2) At what point does the curve y = e x have a maximal curvature? What is the maximal curvature? (3) Find the curvature and the torsion of the curve r ( t ) = ( t, sin t, cosh t ) at t = 0. (4) Find tangential and normal components of the acceleration for r ( t ) = ( t,t 2 ,t 3 ) at
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Unformatted text preview: t = 1. (5) Find the limit or show that it does not exist: lim ( x,y ) → (1 , 2) ( x-1) 2 ( y-2) x 2 + y 2-2 x-4 y + 5 . (6) Find the linearization of f ( x,y ) = xe xy at (1 , 0) and use it to approximate f (1 . 02 ,-. 01). (7) Find the tanget plane to the surface 4 x 2 y 2 z + 3 xyz 3 = 7 at (1 , 1 , 1). (8) Show that u = f ( x + at ) + g ( x-at ) where f,g are twice di±erentiable satisfies the wave equation u tt = a 2 u xx . (9) Given the equation x 2 y + y 3 = 1, use implicit di±erentiation to find dy dx and d 2 y dx 2 . (10) Problem 34 on page 917. (11) Problem 38 on page 925....
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