MATH111-200530-EX02 - (a) (2 marks) f θ 10 tan θ (b) (4...

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MATH111-002 200530 Midterm 2 Edward Doolittle Wednesday, November 2, 2005 Please do each of the following questions. The entire exam is worth 45 marks. You should be able to earn about 1 mark per minute and have 5 minutes left over at the end to check your work. A non-programmable calculator is permitted. 1. For each of the following equations, find a value of x (to four decimal places) which satisfies the equation. (a) (2 marks) log 2 x 1 4 (b) (4 marks) csc arccos x 1 25 2. Calculate the derivatives of the following functions.
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Unformatted text preview: (a) (2 marks) f θ 10 tan θ (b) (4 marks) g x tan 1 x a ln x a x a 3. (5 marks) Use logarithmic differentiation to find the derivative of y 4 x 2 1 x 2 1 . 4. Evaluate the following integrals. (a) (5 marks) 4 2 1 x x 2 x 2 dx (b) (5 marks) 2 tan θ sec 2 θ d θ 5. Find the limits (a) (5 marks) lim x e 4 x 1 4 x x 2 (b) (5 marks) lim x cos x 1 x 2 6. (4 marks) Evaluate dx x 1 x . 7. (4 marks) Find d dx 2 x ln x e t 2 dt ....
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This note was uploaded on 01/12/2010 for the course CALC 111 taught by Professor Edwarddoolittle during the Summer '05 term at University of California, Berkeley.

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