Test 2 - Name Test#2 Limits Continuity Derivatives Find the...

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Name: ______________ Test #2 Limits, Continuity & Derivatives Find the derivative of the following functions: 1. f x = x 10 2. g x = 1 x 3 3. y = e x 4. h x = 25 5. f t = ln t 6. f x = 12 x 7. f x = 3 x 8. V x = π 2 9. r s = log 5 s 10. f x = x ln x − x 11. y = 5 x 3 x 2 2 x 12. P t = ln t 3 Find the indicated limit of the functions: For #13 and #14, let f x = { 9 x 2 3 x x 0 AND x ≠− 3 9 x 2 3 x x 0 a x =− 3 13. Find lim x 0 f x Is this function continuous at x = 0? Why, or why not? 14. For what value of a would make this function continuous at x = -3? 15. State the definition of the derivative for a function f ( x ). Use this definition to find the derivative of the function f x = x 2
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16. For the function f x = 6 x x 2 , find the equation of the line tangent to the graph of this function a x = 2. For what value(s), if any, is the line tangent to this curve horizontal?
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