Fiesta 5
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AP CALCULUS AB | 2008 | Shubleka | Fiesta # 5
Name________________________
Please write your answers neatly on a separate sheet. Show all your work for full credit. Problem 1: a) Find the local linearization of f ( x) = sin x near x = 0 , then use it to approximate sin (0.2). b) Find a quadratic function g ( x) such that g (0) = f (0), g '(0) = f '(0), and g "(0) = f "(0), then use it to approximate sin(0.2). c) Compare your estimations to the “true sin(0.2)”. Problem 2 Find the derivative of the function. Explain the rules as you apply them. a)
f ( x) =
b)
f ( x) = sin(cos(sin x))
cos π x sin π x + cos π x
Problem 3 Suppose f ( x) is a differentiable function on \ . Let F ( x) = f ( xα ) and G ( x) = [ f ( x)] . Find an α
expression for: a) F '( x) b) G '( x)
There are three kinds of lies: lies, damned lies, and statistics. – Benjamin Disraeli
Name________________________
Please write your answers neatly on a separate sheet. Show all your work for full credit. Problem 1: a) Find the local linearization of f ( x) = sin x near x = 0 , then use it to approximate sin (0.2). b) Find a quadratic function g ( x) such that g (0) = f (0), g '(0) = f '(0), and g "(0) = f "(0), then use it to approximate sin(0.2). c) Compare your estimations to the “true sin(0.2)”. Problem 2 Find the derivative of the function. Explain the rules as you apply them. a)
f ( x) =
b)
f ( x) = sin(cos(sin x))
cos π x sin π x + cos π x
Problem 3 Suppose f ( x) is a differentiable function on \ . Let F ( x) = f ( xα ) and G ( x) = [ f ( x)] . Find an α
expression for: a) F '( x) b) G '( x)
There are three kinds of lies: lies, damned lies, and statistics. – Benjamin Disraeli
