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Sample-free-response-midterm

Sample-free-response-midterm - Math 1314 ONLINE Review for...

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Math 1314 – ONLINE Review for midterm Sample free response questions 1. Suppose 2 1, 2 ( ) 3, 2 5 2, 5 x x f x x x x + < - = - - Use the three-part test for continuity at a point to determine if the function is continuous at x = -2 and at x = 5. If the function is not continuous at one (or both) of the points, be sure you state which one of the three parts is not satisfied. State the condition itself (i.e., not I, II or III). 2. Use the limit definition of the derivative (four-step process) to find the derivative: 2 6 3 ) ( 2 + - = x x x f 3. Find the first derivative: 4 3 ) ( 2 2 - = x x x f 4. Find the first derivative: x x x f 3 ) ( 2 - = 5. Find the first and second derivatives: ( 5 2 5 2 ) ( + = x x f 6. Find the first derivative: ( 4 3 2 3 2 ) ( + = x x x f 7. Find the first derivative: 2 4 3 ( ) x f x x e = 8. Find the first derivative: 3 2 7 ( ) ln 3 5 x f x x + = + 9. Find the first derivative: 2 5 ( ) ln(3 ) x f x x e = 10. Suppose you conduct a population study (note: population grows exponentially). At the beginning of the study, the population is 1.6 million people. Two years later, the population is 1.79 million people. a. Find the growth constant,
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