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
 Irrational number, 400foot

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