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21 Apr 2018

1. (a) What is the derivative of f(x) = ? + 2.+ 7? (2 marks) (b) Verify your answer from part (a) by calculating the derivative using the limit definition. (3 marks) (c) What is the 2nd order Taylor polynomial for f(x) at r= 1? (5 marks)

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Lelia Lubowitz
Lelia LubowitzLv2
22 Apr 2018
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8. [20 marks] Lct f(x) = r. a) (4 marks Give definition for the derivative f'(2) as a limit. b) [16 marks] Compute f'(2) from the limit. No marks will be given for applying differentiation rules.

1. (10 marks) (a) Carefully state the definition of the derivative of a function f(x) at a point (b) Use the definition of the derivative from part (a) to compute f'(1) for f(x) = 32 -1 NO CREDIT WILL BE GIVEN FOR ANY OTHER METHOD (c) Find the equation of the tangent line to the graph off at the point (1, ).

Answer all questions in spaces provided. Show all your work. Any answer in Part B without proper justification may receive very little or no credit. Use the back of each page for rough work. Marks for each question are indicated by []. 1. Let f(x) = x2. Find f'(2) from first principles, i.e. by using only the definition of the derivative.

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