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Mercer County Community College Prof. Porter MAT151 NAME:____________________ 1. What is Calculus? What is varying in calculus? What is the derivative? 2. Use the δ-ε definition of limits to show that lim4 x 3 is 11. x2 Answer:____________________ 3. Evaluate the limit: lim x 3 x 2 5x 6 x2 9 Answer:____________________ Explain on when the function is continuous . f ( x) x 2 5x 6 x2 9 Answer:____________________ When is the function removable discontinuous? Answer:____________________ Practice Exam 1 Ax 7 x 2 4. Given the function, find A so that the function is continuous: f ( x) 2 x2 x Answer:____________________ Give a qualitative graph of the continuous function. 5. Evaluate the limit lim f ( x) x a A 0 1 2 3 4 lim f ( x) x a 6. Given the same graph above, determine f’(x) approximately at 1, 2, 3, 0 X= 1 2 3 4 ∞ f’(x) ∞ 7. h(t) = t (2 – t) + 3 represents the height of a ball at time t. Evaluate the function at 0 and 2 and use that information to find the average speed of the ball between t = 0 and t = 2. Answer:_________________ Find the instantaneous speed at t = 1 for this problem. Answer:_________________ 8. Use the definition of derivative to find f’(x) if f(x) = x( x + 1) Be sure to give f(x+h) clearly. Answer:____________________________ (No credit for just answer- must use definition!) 9. Find f’ of the following: f ( x) x sin( / 3) Answer:____________________________ f ( x) 5 x4 Answer:___________________________ 10. Evaluate the limit .9 x 20 5 x 6 x x 20 9 a. lim Answer:____________________ .9 x 200 5 x 6 x x 20 9 b. lim Answer:____________________ .9 x 5 x 6 x x 200 9 20 c. lim Answer:____________________ .9 x 5 x 6 x 20 9 21 d. lim x Answer:____________________ 11. Given the data, perform a quartic regression and determine the max/ mins. Year: Salary: 8 35 10 45 12 46 12. Use the same data to determine the left end limit at infinity 13 48 15 54