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In Exercises 3-16, find the limit. 3. lim x* 4. lim (3x+2) (a) lim glr) (a) lim flx) x→1 5. lim (2x2 + 4x +1) 6. lim (b) lim g(x) (b) lim fa) 2x 5 7. lim 8. lim -3x+3 10. lim +23 In Exercises 25-28, find the limit of the function (if it exists). Write a simpler function that agrees with the given function at all but one point. Use a graphing utility to confirm your result. 9. lim sin x x→ π/2 11. lim sec 2 12. lim sin 25. im 26. l lim 13. lim tan( ) 15.n 3x e) 14. in , 14. lim cos x lim (x+4)ln(r+6) -4 x-16 x→3 27, 28. im 16, lim e-r sin π.x x→ 1 In Exercises 29-36, find the limit (if it exists). In Exercises 17-20, find the limits. 17. fx) 18. f(x) = x + 7, g(x) = x2 19. f(x) = 4-2, g(x)-- 30. limx+ 6 32. limx 3 5-x, gx)- 29. lim ^-25 (a) limfx)(b) lim gx) lim g(fx)) (a) lim, /x) (ms() lim,ga) (a)(b(c) lim) 31. lim 33. lim 35. lim 2(r +Ar)-2

111 Review Exercises See CalcChat.com for tutorial help and worked-out solutions to odd-numbered exercises 2, determine recalculus or e solved using uire calculus, or numerical 15. limI 17. lim, 72 4 19. limx 4 16. lim 2 1 18. lim16 20. lim 4 t2 x?-212-4 x-3-1 4+x-2 im D- 22. lim (1/s)- (3, 9) along the 21. lim s-+0 3, 9) along the 23. lim 24. lim tan x x-+0 sin x ises 3 and 4, the limit. Use TX '25. lim eI sin 26. lim Indr 1)2 26. li ln(x-1) x-il n your result.27. limsinl (6+Al(1/2) Ar--0 Ax [Hint: sin(? + ?) = sin ? cos ? + cos ? sin ?] 28. lim cos(r+dr)+1 01 3.1 [Hint: cos(e+ ?) cos ? cos ?-sin ? sin ?] Evaluating a Limit In Exercises 29-32, evaluate the given lim f(x)6 and lim g(x).

e +e-2 Calculate the limit: lim 2-+0 1- cos(8) 1- cos(8x a) O1 b) O c) 32 d) 0 e 32 16 Question 16 Calculate the limit: lim (e* +1) a) Oe2 b) e3 c) -e d) 0 3 e'