soln-prac-mid2

soln-prac-mid2 - Solutions to Practic Midterm 2 1 Find the...

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Unformatted text preview: Solutions to Practic Midterm 2 1 Find the normal line to the curve x + y = e 2 y at the point (1 , 0) . Solution We need to find dy dx so that we can find the slope of the normal line. Using implicit differentiation, we find 1 2 x + y (1 + y ) = 2 y e 2 y . We plug in the point (1 , 0) and solve for y . Doing so, we get y = 1 3 . Thus the normal line has slope- 3, and its equation is y =- 3( x- 1) . (Note, you could have also done implicit diff to x + y = e 4 y yielding 1 + dy dx = 4 ye 4 y dy dx and then plugging in y = 0 yields 1 + dy dx = 4 dy dx .) 2 Find ds dw if t = Tan- 1 (ln w ) and s = 2 t ( t + t ) 1 / 3 . Solution By the Chain Rule, ds dw = ds dt dt dw . ds dt = 2( t + t ) 1 / 3- 2 t 1 3 ( t + t )- 2 / 3 1 + 1 2 t ( t + t ) 2 / 3 dt dw = 1 1 + (ln w ) 2 1 w 1 2 w Thus ds dw = 2( t + t ) 1 / 3- 2 t 1 3 ( t + t )- 2 / 3 1 + 1 2 t ( t + t ) 2 / 3 1 1 + (ln w ) 2 1 w 1 2 w 3 Find the derivative with respect to the appropriate independent variable.Find the derivative with respect to the appropriate independent variable....
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soln-prac-mid2 - Solutions to Practic Midterm 2 1 Find the...

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