m19Am2f07

m19Am2f07 - 1. (25 points) Compute the requested...

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1. (25 points) Compute the requested derivatives of the following functions: (a) dy dx for y = cos(cosh x ) (b) dz dt for z = q t + t 2 + e 2 t (c) f 0 ( x ) for f ( x ) = tan - 1 (1 - ke x ), where k = k ( x ) is a function of x . (d) dy dt for y = λ 2 π e - ωt 2 + α 0 , where λ,ω and α 0 are constants. (e) dy dx for y = x x , where 0 x . 1
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2. (10 points) Find the equation of the tangent line to the curve (called astroid) given by x 2 3 + y 2 3 = 4 at the point (3 3 , - 1). Express your answer in the form y = mx + b . 3. (10 points) Show that e x x + 1 for x VERY close to 0. In other words, show that the linearization of f ( x ) = e tan x for a = 0 is given by L ( x ) = x + 1. (Extra Credit, 3 points) Give a quadratic approximation to f ( x ) for a = 0. 2
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4. (10 points) (a) (7 points) Carefully state the Mean Value Theorem (MVT). (b) (3 points) The function f ( x ) = | x | on the interval [ - 1 , 1] does not satisfy the conclusion of the MVT. Explain why this does not contradict the MVT.
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m19Am2f07 - 1. (25 points) Compute the requested...

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