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Unformatted text preview: Answer: Note that 36 days is 1 / (10) of a year, the unit used here. So, the change will be about f ′ (0) · . 1 =. 2 and hence after 36 days, there should be about 41 . 8 Millions. 9) Let f ( x ) be equal to f ( x ) = cos( x ) x . Calculate f ′ ( x ). Answer: f ′ ( x ) =x sin( x )cos( x ) x 2 . 10) Calculate the limit lim x → sin(2 x 3 + 3 x 2 ) x 3 + x Answer: We have sin(2 x 3 + 3 x 2 ) x 3 + x = sin(2 x 3 + 3 x 2 ) 2 x 3 + 3 x 2 · 2 x 3 + 3 x 2 x 3 + x . But the limit of sin(2 x 3 + 3 x 2 ) 2 x 3 + 3 x 2 as x goes to 0 is 1. (When x goes to 0, we have that 2 x 3 + 3 x 2 also goes to 0. ..) Also, the limit 2 x 3 + 3 x 2 x 3 + x = 2 x 2 + 3 x x 2 + 1 is 0 / 1 = 0 as x → 0. Hence, the answer is 1 · 0 = 0....
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 Fall '08
 N/A
 Math, Calculus, Sin, Equals sign, ASCII, relational operator

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