Homework 7 - (a) (2 Points) a ( x ) = ln p x x + 1 P . (b)...

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INSTRUCTOR: JOS ´ E MANUEL G ´ OMEZ Homework 7. Due date Wednesday October 26, 2011 Please show all your work. (1) (5 Points) Suppose that f and g are diferentiable Functions such that f (1) = 2 , f (2) = 1 , f (1) = 2 , f (2) = 1 g (1) = 2 , g (2) = 2 , g (1) = 3 , g (2) = 1 . (a) (1 Points) IF a ( x ) = f 1 ( x ) compute a (2). (b) (2 Points) IF b ( x ) = f 1 ( x ) compute b (4). (c) (1 Points) IF c ( x ) = f g 1 ( x ) compute c (2). (d) (1 Points) IF d ( x ) = ln( f ( x )) compute d (2). (2) (5 Points) Use the limit de±nition oF the derivative to show that d dx cos( x ) = sin( x ) . Remark: No credit will be given to computations that don’t use the limit de±nition oF the derivative. (3) (5 Points) Consider the Function f ( x ) = 3 x . (a) (3 Point) ²ind the linear approximation oF f at x = 2. (b) (2 Points) Use the above to approximate 3 8. (4) (10 Points) ²ind the derivative oF the Following Functions.
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Unformatted text preview: (a) (2 Points) a ( x ) = ln p x x + 1 P . (b) (2 Points) b ( x ) = cos( x 2 ) ln( x + 2) . (c) (2 Points) c ( x ) = e tan-1 ( x ) . (d) (2 Points) d ( x ) = sec 2 ( x ln( x )) . (e) (2 Points) e ( x ) = x 2 tan( x ) . 1 2 INSTRUCTOR: JOS E MANUEL G OMEZ (5) (5 Points) A scientist wants to study a certain kind of radioactive isotope present in a fossil. Let P ( t ) denote the amount (in grams) of this isotope present in the fossil t-years after its discovery. It is known that when the rock was discovered the fossil had 2000 grams of this isotope and that the half life of this isotope is 150 years. (a) (3 Points) Find an equation for P ( t ). (b) (2 Points) Find P ( t )....
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Homework 7 - (a) (2 Points) a ( x ) = ln p x x + 1 P . (b)...

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