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(6) 1. Compute the derivatives of the following functions:

a) xe

cos x

b) tan

3

(x

3

)

(8) 2. Compute the following limits:

a) lim

x!0

e

5x

5x1

x

2

b) lim

x!1

x

2

+1

x+1

(13) 3. Find an equation for the line tangent to the graph of lny+x

3

+2xy = 10 at the point

(2;1).

(8) 4. A certain function f(x) is dened and dierentiable for all real numbers x. If f(1) = 2

and jf

0

(x)j 3 for 1 <x<3, what is the largest possible value of f(3)? What is the

smallest possible value of f(3)? Give brief explanations of your answers.

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