MA 112 - 01PC Applied Calculus for Aviation Summer 2022 Exam 1 Review Exercises Remark: Do not rely solely on this problem set to study for the exam. It is highly recommended to do the Exam Review on MyMathLab, and also study the class notes and previous homework. 1. The graph of f (x) is given below. Use the graph to answer questions (a)-(d) below. (a) Compute the following. If it does not exist (DNE), explain why. (i) lim f (x) = x→−8− (ii) lim f (x) = (iii) lim f (x) = x→−8 x→−8+ (iv) f (−8) = (b) Compute the following. If it does not exist (DNE), explain why. (i) lim− f (x) = x→6 (ii) lim+ f (x) = (iii) lim f (x) = x→6 x→6 (iv) f (6) = (c) Compute the following. If it does not exist (DNE), explain why. (i) lim f (x) = x→10− (ii) lim f (x) = (iii) lim f (x) = x→10 x→10+ (d) State the value(s) of x at which f is discontinuous. 2. Compute lim (x5 + 2x2 − 3x2 − x + 9) x→−1 3. Compute x3 − 8x + 3 x→0 x2 + x − 1 lim 4. Compute x2 − 3x − 4 x→4 x−4 lim 5. Compute lim x→2 1 x − 12 x−2 6. Compute x2 − x − 6 x→1 (x + 1)2 lim (iv) f (10) = 7. Compute x3 + x2 − x + 10 x→∞ 1 − x3 lim 8. Compute lim x→∞ 20x + 3 x2 + x + 1 9. Compute 20x3 + 3 x→∞ x2 + x + 1 lim 10. Use the definition of the derivative to compute f 0 (x) where f (x) = 3x2 + x − 5. 11. Use the definition of the derivative to compute f 0 (x) where f (x) = 4x + 7. For questions 12–20, compute the derivative of each function. You do not need to simplify. 1 12. y = x5 + x6 − 7 5 13. f (x) = −2x5 + 9x4 − 14. g(t) = √ x − 9x 5 − 100 t4 15. f (x) = (1 + x5 )(5x3 + 1) t4 − 1 t4 + 1 √ 17. f (x) = x3 + x 16. h(t) = 18. f (x) = (4x3 + 9x2 − 1)9 19. h(t) = (3x2 1 + 1)5 20. g(z) = 8z 3 (4z + 9)3 21. Find the slope of tangent line to the curve y = 22. For the following equations, compute dy dx x2 − 1 at (1, 1). x2 + 1 using implicit differentiation. (a) xy 4 + y 3 = x2 + 3y (b) xy = y 3 − 1 2