1. We know from our lessons that In(r)]' = Let us consider a new function, In(r)...

  

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1. We know from our lessons that In(r)]' = Let us consider a new function, In(r) if a>0 In r| = |In(-r) if r <0 (a) (1 mark) State the domain of this function. (b) (2 marks) Determine the derivative of In r. (HINT: Break the problem into two parts, based on the values of a. 2. (3 marks) If f(r) = 1 determine f'(1). Be careful to show all your work. 3. (4 marks) The atmospheric pressure at an altitude of r kilometers above sea- level is approximately e/8 millibars. A rocket is rising at a rate of 8 kilometers per second vertically. At what rate is the atmospheric pressure changing (in millibars per second) when the altitude of the rocket is (a) 8 kilometers? (b) 64 kilometers? 1. We know from our lessons that In(r)]' = Let us consider a new function, In(r) if a>0 In r| = |In(-r) if r <0 (a) (1 mark) State the domain of this function. (b) (2 marks) Determine the derivative of In r. (HINT: Break the problem into two parts, based on the values of a. 2. (3 marks) If f(r) = 1 determine f'(1). Be careful to show all your work. 3. (4 marks) The atmospheric pressure at an altitude of r kilometers above sea- level is approximately e/8 millibars. A rocket is rising at a rate of 8 kilometers per second vertically. At what rate is the atmospheric pressure changing (in millibars per second) when the altitude of the rocket is (a) 8 kilometers? (b) 64 kilometers?

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