# GHW3 - [10,15(c If is the fat calories used at time t what...

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MATH 2413 Graded Homework #3 GHW3 17 September 2011 Due 9/26 in Lecture Work is to be done in a Blue book per the syllabus 1. Evaluate the limit (a) (3 pts) + 2 3 cos lim x x x π (b) (7 pts) 2 4 7 5 lim x x x x + + 2. (6 pts) Use the formula a x a f x f m a x = ) ( ) ( lim to find the slope of the tangent line to the graph of at the point where the x -coordinate is 2. 2 7 5 ) ( x x x f = 3. (3 pts) JB records the number of Total Calories and Fat Calories burned at 5 minute intervals during a treadmill workout. Round numerical responses to 2 decimal places and include the units. Time (min) 0 5 10 15 20 Tot Calories 0 41.5 91.5 139 191 Fat Calories 0 13.3 28.2 43.6 59.3 (a) Find the average rate of Fat Calories burned over the entire period. (b) Compute the average Total Calories used over the intervals [5,10] and
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Unformatted text preview: [10,15]. (c) If is the fat calories used at time t , what is the meaning of the derivative of f ? ) ( t f What are its units? 4. (8 pts) Find an equation of the line tangent to the curve x x f + = 3 1 ) ( at ) , 1 ( 4 1 . Use the formula h a f h a f a f h ) ( ) ( lim ) ( ' − + = → to compute the slope. 5. (8 pts) (a) Use the definition of the derivative h x f h x f x f h ) ( ) ( lim ) ( ' − + = → to find the derivative of the function 4 ) ( − = x x f . (b) Find the interval(s) where f is differentiable. (Use interval notation.) 6. (4 pts) Express the 2nd and 5th derivatives of ) ( x f z = in (a) Liebnitz notation (b) Function notation...
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