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Unformatted text preview: be going when it hits you? Where was the chandelier when it was moving with half that speed? 4. Derive the derivatives of tan x , cot x , sec x , and csc x when given only that d dx sin x = cos x d dx cos x = sin x. 5. a) Show that lim h f ( a + h ) f ( a ) h = lim x a f ( x ) f ( a ) x a . b) Use the above fact to calculate: i) lim x 8 x 4 / 3 16 x 8 iv) lim x 1 x 2 + x ( x + 2)( x + 1) ii) lim x 2 (6 + x ) 2 / 3 4 x 2 iii) lim x 1 x 100 1 x 1 v) lim x 1 x 3 2 x 2 + 2 x 1 x 1 6. If f + g is diFerentiable at a , are f and g necessarily diFerentiable at a ? If f g and f are diFerentiable at a , what conditions on f imply that g is diFerentiable at a ?...
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 Spring '08
 Grether

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